Enter one equation or expression, keep every sign and denominator visible, and review the exact answer together with the algebraic move used at each step.
Result
The equation has one solution. Distribute, combine like terms, collect the x-terms, and divide by the remaining coefficient.
x=4
Conditions
x is treated as a real variable.
The entered equality is interpreted exactly as written.
No denominator in the original expression may equal zero.
Steps
Distribute across the parentheses Multiply both terms inside the parentheses by 2.6x−8+5=3x+9
Combine like terms The constants on the left combine to negative 3.6x−3=3x+9
Collect the variable terms Subtract 3x from both sides, then add 3 to both sides.3x=12
Divide by the coefficient Divide both sides by 3 to isolate x.x=4
✓
Independent check
Substitution gives 2(3(4)-4)+5=21 on the left and 3(4)+9=21 on the right.
Scope
What this solve covers
Use this solver for core algebra tasks that can be checked by substitution, expansion, or equivalence. The result should tell you whether it solved an equation, simplified an expression, or factored a polynomial, because those are different mathematical jobs.
Solve linear equations
Balance equations with distribution, fractions, like terms, and variables on both sides.
Examples: 2x+7=19, 3(x-2)=2x+5, x/3+2=5
Solve quadratic equations
Find exact roots by factoring when possible or by applying the quadratic formula.
Examples: x^2-5x+6=0, 2x^2+x-3=0
Factor polynomials
Extract a greatest common factor and recognize trinomials, perfect squares, and differences of squares.
Examples: 6x^3+9x^2, x^2-16, x^2+7x+12
Simplify expressions
Use distribution, exponent rules, and like terms while preserving restrictions from the original expression.
Examples: 3(2x-1)-4(x+2), x^3x^2/x
How to use it
Enter enough information for one clear task
1
Enter the complete problem
Include the equals sign when solving and use parentheses to make grouping unambiguous. Enter an expression without an equals sign only when you want to simplify or factor it.
2
Confirm the interpreted task
Check whether the page identified solve, simplify, or factor. Correct missing parentheses or restrictions before trusting the steps.
3
Follow the named transformations
Read the reason for each line, not only the changed expression. Equivalent transformations preserve the solution set unless a restriction is introduced.
4
Check the final form
Substitute equation solutions into the original equation, expand a factorization, or compare equivalent simplified forms under the stated conditions.
Worked inputs
Examples to try
Use these examples to recognize the method, compare equivalent forms, and check your own work.
Linear equations
One-step linear equation
Subtract 7, then divide by 2.
2x+7=19
Expected result
x=6
Distribution before solving
Distribute 3 and collect the x-terms.
3(x−2)=2x+5
Expected result
x=11
Show more linear equations examples
Equation with a fraction
Subtract 2 and multiply both sides by 3.
3x+2=5
Expected result
x=9
Variables on both sides
Move variable terms to one side and constants to the other.
5x−4=2x+11
Expected result
x=5
Quadratics and factoring
Quadratic solved by factoring
Factor the trinomial and apply the zero-product property.
x2−5x+6=0
Expected result
x∈{2,3}
Quadratic with unequal leading coefficient
Factor into two binomials and set each factor to zero.
2x2+x−3=0
Expected result
x∈{1,−23}
Show more quadratics and factoring examples
Difference of squares
Use a squared term minus a squared constant.
x2−16
Expected result
(x−4)(x+4)
Monic trinomial
Find two integers whose product is 12 and sum is 7.
x2+7x+12
Expected result
(x+3)(x+4)
Simplifying expressions
Simplify by distribution
Distribute both coefficients, then combine like terms.
3(2x−1)−4(x+2)
Expected result
2x−11
Linear equation with two distributions
Distribute, combine like terms, and isolate x.
2(x+1)−3(x−2)=7
Expected result
x=1
Show more simplifying expressions examples
Greatest common factor
Extract the greatest numerical and variable factor.
6x3+9x2
Expected result
3x2(2x+3)
Simplify powers with a restriction
Add exponents in the numerator, then subtract the denominator exponent.
xx3x2
Expected result
x4,x=0
Complete example
Solve a quadratic by revealing its factors
The equation is already in standard form. Factoring is efficient because the constant and middle coefficient have a simple integer pair.
x2+x−6=0
1
Find the factor pair
The numbers 3 and negative 2 multiply to negative 6 and add to 1.
3(−2)=−6,3+(−2)=1
2
Factor the quadratic
Use the pair as the constant terms of two binomials.
x2+x−6=(x+3)(x−2)
3
Apply the zero-product property
A product is zero when at least one factor is zero.
x+3=0orx−2=0
x∈{−3,2}
Verification: Substituting x=-3 gives 9-3-6=0, and substituting x=2 gives 4+2-6=0.
Avoidable errors
Common mistakes and how to fix them
Dropping a negative sign during distribution
Problem: -(2x-5)=-2x-5
Why it matters: The negative factor must multiply every term inside the parentheses.
Better approach: Write -(2x-5)=-2x+5 before combining like terms.
Canceling terms across addition
Problem: (x+3)/x=3
Why it matters: Cancellation applies to common factors, not to one term inside a sum.
Better approach: Keep (x+3)/x or rewrite it as 1+3/x, with x not equal to zero.
Dividing by an expression that may be zero
Problem: From x(x-4)=0, divide by x and keep only x=4.
Why it matters: Dividing by x discards the valid case x=0.
Better approach: Use the zero-product property first, giving x=0 or x=4.
Checking only the transformed equation
Problem: Accept every candidate produced after squaring or clearing a denominator.
Why it matters: A non-reversible step or an excluded denominator can introduce an invalid candidate.
Better approach: Substitute each candidate into the original problem and enforce its original restrictions.
Trust the result for the right reasons
Checks, assumptions, and limits
How results are checked
Equation solutions are substituted into the original equation.
Polynomial factorizations are expanded to recover the original polynomial.
Simplified expressions retain restrictions inherited from denominators.
Exact fractions and radicals are kept before any decimal approximation.
When to stop and revise the input
Ambiguous grouping can change the problem, so parentheses must be explicit.
A denominator equal to zero is excluded even if later cancellation hides it.
This page does not turn an expression into an equation when no equals sign is present.
A result outside the supported algebra scope should be reported as unsupported rather than guessed.
Common questions
Solve an algebra problem step by step FAQ
What algebra problems belong in the general solver?
Use it for linear and quadratic equations, polynomial factoring, and expression simplification within the supported scope. A focused calculator is clearer when you already know that you need to solve for x, factor, or apply the quadratic formula.
Why does the solver show an interpreted problem?
Parentheses, fractions, and minus signs can change the meaning of an expression. Confirming the interpreted problem lets you catch a parsing mistake before reading the result.
How can I check an equation solution?
Substitute the proposed value into both sides of the original equation. The value is valid only when both sides are defined and equal.
Why can a simplified answer have a restriction?
Simplification may cancel a factor, but it does not make a previously zero denominator valid. Restrictions belong to the original expression and must remain with the simplified form.
Why might my answer look different from another answer?
Equivalent factored, expanded, fractional, or radical forms can represent the same value. Compare them by expansion, exact arithmetic, or substitution under the stated conditions.
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