Answer
{$-4,-12$}
Work Step by Step
Using the rules of factoring trinomials, we obtain:
$x^{2}+16x+48=0$
$x^{2}+4x+12x+48=0$
$x(x+4)+12(x+4)=0$
$(x+4)(x+12)=0$
$(x+4)=0$ and $(x+12)=0$
$x=-4$ and $x=-12$
Therefore, the solution set is {$-4,-12$}.