Solve: x² − 5x + 6 = 0

x = 2 or x = 3

Factor the quadratic: (x − 2)(x − 3) = 0. Setting each factor to zero gives x = 2 or x = 3. Check: 4 − 10 + 6 = 0 ✓ and 9 − 15 + 6 = 0 ✓.

Understanding Algebra questions

Algebra questions ask you to work with unknowns using the same balance rules on both sides of an equation. Once you can isolate a variable reliably, most school-level algebra becomes mechanical rather than tricky.

How to approach it

1. Simplify each side separately: expand brackets and combine like terms.
2. Move variable terms to one side and constants to the other using inverse operations.
3. Divide by the coefficient of the variable to isolate it.
4. Substitute the answer back into the original equation to verify it.

Common mistakes to avoid

• Applying an operation to only one side of the equation.
• Losing the sign when moving a negative term across the equals sign.
• Combining unlike terms such as x and x².

Where it appears: Core to CBSE Class 6–10 maths, IGCSE, IB MYP and every competitive aptitude paper.

• Example: x² − 7x + 12 = 0 → (x − 3)(x − 4) = 0 → x = 3 or 4.
• Example: x² + 5x + 6 = 0 → (x + 2)(x + 3) = 0 → x = −2 or −3.