Answer
$-2$ and $-3$
Work Step by Step
See example 2 in R-2 (factoring trinomials).
We search for factors of 6 that add up to 5 ....
2$\times$3=6, 2+3=5
so
$x^{2}+5x+6=0$
$(x+2)(x+3)=0$
We apply the zero product rule
(if the product is zero, at least one of the factors is zero)
$x=-2 \ \ $ or $\ \ x=-3$
solutions: $-2\ \ $ and $-3$
