#### Answer

$x=\{-10,-3\}$

#### Work Step by Step

Equating each factor to zero (Zero Product Principle), then the solutions to the given equation, $
(x+3)(x+10)=0
,$ is
\begin{array}{l}
x+3=0
\\\\
x=-3
,\\\\\text{OR}\\\\
x+10=0
\\\\
x=-10
.\end{array}
Hence, $
x=\{-10,-3\}
.$