Factorise the left hand side by finding two numbers that multiply to give -12 and add to give -1.

-4 and 3

The factors are $(x - 4)$ and $(x + 3)$ , rewrite the equation by multiplying them together and set equal to 0.

$\begin{array}{rcl} (x - 4) (x + 3) & = & 0 \end{array}$

Brackets written with any factors of -12 [1]
Brackets written with correct factors of -12 [1]

The roots can be found by setting each factor equal to 0 and solving separately.

If $(x - 4) (x + 3) = 0$ then either $x - 4 = 0$ or $x + 3 = 0$ .

For $x - 4 = 0$ the solution is:

$\begin{array}{rcl} x - 4 & = & 0 \\ + 4 & = & + 4 \\ x & = & 4 \end{array}$

For $x + 3 = 0$ the solution is:

$\begin{array}{rcl} x + 3 & = & 0 \\ - 3 & = & - 3 \\ x & = & - 3 \end{array}$

$x = 4 and x = - 3$ [1]

Solving Quadratic Equations (Edexcel GCSE Maths: Foundation)

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