Answer
$\{-5,-3\}$
Work Step by Step
Using the factoring of trinomials in the form $x^2+bx+c,$ the $\text{
equation
}$
\begin{array}{l}\require{cancel}
x^2+8x+15=0
\end{array} has $c=
15
$ and $b=
8
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
3,5
\right\}.$ Using these two numbers, the factored form of the $\text{
equation
}$ above is
\begin{array}{l}\require{cancel}
(x+3)(x+5)=0
.\end{array}
Equating each factor to zero (Zero Product Property) and solving for the variable result to
\begin{array}{l|r}
x+3=0 & x+5=0
\\
x=-3 & x=-5
\end{array}
Hence, the solution set of the equation $
x^2+8x+15=0
$ is $\{-5,-3\}$.
