# How do you solve X ( X+9) = 4 (X+6) by factoring?

Aug 21, 2015

The solutions are
color(blue)(X=3
color(blue)(X=-8

#### Explanation:

$X \left(X + 9\right) = 4 \left(X + 6\right)$

${X}^{2} + 9 X = 4 X + 24$

${X}^{2} + 5 X - 24 = 0$

We can Split the Middle Term of this expression to factorise it and thereby find solutions.

In this technique, if we have to factorise an expression like $a {x}^{2} + b x + c$, we need to think of 2 numbers such that:

${N}_{1} \cdot {N}_{2} = a \cdot c = 1 \cdot - 24 = - 24$
AND
${N}_{1} + {N}_{2} = b = 5$

After trying out a few numbers we get ${N}_{1} = 8$ and ${N}_{2} = - 3$
$8 \cdot - 3 = - 24$, and $8 + \left(- 3\right) = 5$

${X}^{2} + 5 X - 24 = {X}^{2} + 8 X - 3 X - 24$

${X}^{2} + 8 X - 3 X - 24 = 0$

$X \left(X + 8\right) - 3 \left(X + 8\right) = 0$

$\left(X - 3\right) \left(X + 8\right) = 0$

We now equate factors to zero.
X-3=0, color(blue)(X=3
X+8=0, color(blue)(X=-8
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