#### Answer

$x=\{ -7,-3 \}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given equation, $
(x+7)(x+3)=0
,$ use the Zero-Factor Property by equating each factor to zero. Then solve each equation.
$\bf{\text{Solution Details:}}$
Equating each factor of the equation above to zero (Zero-Factor Property), then
\begin{array}{l}\require{cancel}
x+7=0 \text{ OR } x+3=0
.\end{array}
Using the properties of equality to solve each of the equation above results to
\begin{array}{l}\require{cancel}
x+7=0
\\\\
x=-7
\\\\\text{ OR }\\\\
x+3=0
\\\\
x=-3
.\end{array}
Hence, the solutions are $
x=\{ -7,-3 \}
.$