Type any algebra problem below and get a clear, step-by-step solution in seconds. From linear equations to quadratics and systems, our free algebra solver shows the full working so you actually learn how to get the answer.
Free · Step-by-step worked solutions · Works on any device
What this algebra solver does
This algebra solver takes the equation or expression you enter and walks through it one step at a time, just like a patient tutor would. Instead of only handing you a final number, it shows each move so you can follow the logic and repeat it on your own homework.
It handles a wide range of common algebra tasks, including:
- Linear equations in one variable, such as \( 3(2x - 5) = 4x + 7 \).
- Quadratic equations solved by factoring, completing the square, or the quadratic formula.
- Systems of equations using substitution or elimination.
- Simplifying expressions, combining like terms, and expanding brackets.
- Inequalities, ratios, exponents, and basic factoring.
Enter problems as plain text or build them with the equation editor. Powered by our AI engine, the solver reads your input, chooses a sensible method, and lays out the reasoning clearly.
Worked examples
Example 1: A linear equation
Solve \( 3(2x - 5) = 4x + 7 \).
First, expand the bracket on the left:
$$ 6x - 15 = 4x + 7 $$Move the variable terms to one side and the constants to the other:
$$ 6x - 4x = 7 + 15 $$ $$ 2x = 22 $$Divide both sides by 2:
Quick check: \( 3(2\cdot 11 - 5) = 3(17) = 51 \) and \( 4\cdot 11 + 7 = 51 \). Both sides match.
Example 2: A quadratic equation
Solve \( 2x^2 + 3x - 5 = 0 \) with the quadratic formula, where \( a = 2 \), \( b = 3 \), and \( c = -5 \).
$$ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} $$Find the discriminant first:
$$ b^2 - 4ac = 3^2 - 4(2)(-5) = 9 + 40 = 49 $$Since \( \sqrt{49} = 7 \), substitute back in:
$$ x = \frac{-3 \pm 7}{4} $$This gives two solutions:
$$ x = \frac{4}{4} = 1 \qquad \text{or} \qquad x = \frac{-10}{4} = -\frac{5}{2} $$Common mistake
Watch the signs inside the discriminant. Here \( -4ac = -4(2)(-5) = +40 \), not \( -40 \). A misplaced negative is the most frequent quadratic error.
Example 3: A system of equations
Solve the system \( x + y = 7 \) and \( 2x - y = 2 \) by elimination.
Add the two equations so that \( y \) cancels:
$$ (x + y) + (2x - y) = 7 + 2 $$ $$ 3x = 9 \quad \Rightarrow \quad x = 3 $$Substitute \( x = 3 \) into \( x + y = 7 \):
$$ 3 + y = 7 \quad \Rightarrow \quad y = 4 $$Check the second equation: \( 2(3) - 4 = 2 \). Correct.
How to use the algebra solver
- Enter your problem. Type the equation or expression, or use the equation editor for fractions, exponents, and roots.
- Solve. Press solve and let our advanced AI choose a method and work through the problem.
- Follow the steps. Read each line, check the final answer, and rework the example yourself to lock in the method.
Tip
Always substitute your answer back into the original equation. If both sides are equal, your solution is verified.
Related step-by-step guides
- How to Solve Systems of Equations — compare substitution and elimination with clear examples.
- How to Solve Inequalities Step by Step — including when to flip the inequality sign.
- Factoring Polynomials: A Complete Guide — from common factors to trinomials.
Keep solving
Need a different tool? Try our Equation Solver for any equation type, or branch out with the Calculus Solver when you move on to derivatives and integrals.
