Solving quadratics with the zero-product rule

The common mistake

Factoring when the equation isn't equal to zero, e.g. x² + x = 6 solved as x(x + 1) = 6 → x = 6.

Instead: Move everything to one side first so it equals 0, then factor and solve each bracket.

Worked example with Guide me

Solve x² + x = 6.

1. Sugar · Is one side zero?
   Student · No — subtract 6: x² + x − 6 = 0.
2. Sugar · Factor it.
   Student · (x + 3)(x − 2) = 0.
3. Sugar · When is each bracket zero?
   Student · x = −3 or x = 2.

Answer: x = −3 or x = 2

Try 3 practice questions

1. 1. Solve x² − 5x + 6 = 0.

   Show answer

   x = 2 or x = 3

2. 2. Solve x² = 4x.

   Show answer

   x = 0 or x = 4

3. 3. Solve x² − 16 = 0.

   Show answer

   x = 4 or x = −4

Quick answers

What is the most common mistake with solving quadratics with the zero-product rule?

Factoring when the equation isn't equal to zero, e.g. x² + x = 6 solved as x(x + 1) = 6 → x = 6.

How do I get solving quadratics with the zero-product rule right?

Move everything to one side first so it equals 0, then factor and solve each bracket.

Can you show a worked example?

Solve x² + x = 6. x = −3 or x = 2

Related concepts

• Factoring quadratics into two brackets
• Solving with variables on both sides
• Combining like terms