#### Answer

$x=\left\{ -8,0 \right\}$

#### Work Step by Step

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