#### Answer

$x=\left\{ -5,-3 \right\}$

#### Work Step by Step

Factoring the given equation, $
n^2+8n+15=0
,$ results to
\begin{array}{l}\require{cancel}
(n+3)(n+5)=0
.\end{array}
Equating each factor to zero (Zero Product Principle), then the solutions to the equation, $
(n+3)(n+5)=0
,$ is
\begin{array}{l}\require{cancel}
n+3=0
\\\\
n=-3
,\\\\\text{OR}\\\\
n+5=0
\\\\
n=-5
.\end{array}
Hence, $
x=\left\{ -5,-3 \right\}
.$