A product that is zero
If A × B = 0, then A = 0 or B = 0. That is the whole trick.
- x² − x − 12 = 0
- (x − 4)(x + 3) = 0
- x − 4 = 0 or x + 3 = 0
- x = 4 or x = −3
Notice the signs flip: the bracket (x + 3) gives x = −3. Put each answer back in to check: 16 − 4 − 12 = 0.
Make one side zero first
x² + 2x = 15 cannot be factorised as it stands. Move everything to one side: x² + 2x − 15 = 0, then factorise.
Never divide both sides by x. In x² = 5x, dividing gives x = 5 and loses x = 0. Rearrange instead: x² − 5x = 0, x(x − 5) = 0, so x = 0 or x = 5.
Check with the solver
Pick Quadratic and enter a = 1, b = −1, c = −12. The solver agrees with x = 4 and x = −3. Use it to check your answers, not to replace the working: the marks are for the factorising.