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

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Answer 1 · 2015-08-21T07:31:14

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

$X(X+9)=4(X+6)$

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

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

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 $ax^2 + bx + c$ , we need to think of 2 numbers such that:

$N_1*N_2 = a*c = 1*-24 = -24$
AND
$N_1 +N_2 = b = 5$

After trying out a few numbers we get $N_1 = 8$ and $N_2 =-3$
$8*-3 = -24$ , and $8+(-3)= 5$

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

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

$X(X+8) -3(X+8)=0$

$(X-3)(X+8)=0$

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

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