Answer
{$2,-9$}
Work Step by Step
We use the distributive property in order to put the equation into trinomial form. We then use the rules of factoring trinomials and set the equation equal to zero to solve the equation:
$(x+1)(x+6)=24$
$x(x+6)+1(x+6)=24$
$x^{2}+6x+x+6=24$
$x^{2}+7x+6-24=0$
$x^{2}+7x-18=0$
$x^{2}-2x+9x-18=0$
$x(x-2)+9(x-2)=0$
$(x-2)(x+9)=0$
$(x-2)=0$ or $(x+9)=0$
$x=2$ or $x=-9$
Therefore, the solution set is {$2,-9$}.
