Algebra Calculator - Solve Equations & Factor Step-by-Step
Solve algebra problems step-by-step. Free online algebra calculator for equations, factoring, polynomials, and simplifying expressions for math students.
📝 Try an Example
Click any example to load it, then hit Solve
Format: ax + b = c
💡 Quick Tips
Exponents: Use x^2 for x²
Negative numbers: Use -3x or x - 5
Click examples to auto-fill inputs
Step-by-step: Expand to see how it's solved
Solve equations and work through algebraic problems with detailed explanations. This tool shows each step so you can understand the solution process.
How to Use Algebra Calculator
Solving Linear Equations
Enter your equation in the format "ax + b = c". For example, type "2x + 3 = 7" and click Solve. The calculator isolates x by performing inverse operations, showing each step.
Working with Quadratics
Enter equations like "x^2 - 5x + 6 = 0". The tool applies the quadratic formula, calculates the discriminant, and explains whether solutions are real or complex.
Systems of Equations
Enter two equations with x and y variables. The calculator uses Cramer's rule to find where the lines intersect, providing the solution coordinates.
Calculator Features
Step-by-Step Solutions
See every step from start to finish, not just the answer
Multiple Equation Types
Handle linear, quadratic, and systems of equations
Polynomial Operations
Add, subtract, multiply, and factor polynomial expressions
Inequality Solver
Find solution sets expressed in interval notation
Verification Steps
Confirms answers by substituting back into original equations
Common Calculations & Examples
Example 1: Solve for x
Problem: Find x when 3x - 7 = 14
Steps:
- Add 7 to both sides: 3x = 21
- Divide both sides by 3: x = 7
Explanation: We isolate x by undoing each operation in reverse order. First add 7, then divide by 3.
Example 2: Quadratic with Two Solutions
Problem: Solve x² - 5x + 6 = 0
Steps:
- Identify a=1, b=-5, c=6
- Calculate discriminant: (-5)² - 4(1)(6) = 1
- Apply formula: x = (5 ± 1) / 2
Explanation: The positive discriminant indicates two distinct real solutions. You can verify by factoring: (x-3)(x-2) = 0.
Example 3: System of Two Equations
Problem: Solve: x + y = 5 and 2x - y = 1
Steps:
- Add equations to eliminate y: 3x = 6
- Solve for x: x = 2
- Substitute back: 2 + y = 5, so y = 3
Explanation: The solution represents the point where both lines intersect on a graph.