#### Answer

$\color{blue}{\left\{-4, 0\right\}}$

#### Work Step by Step

Factor out $5x$ to obtain:
$5x(x+4)=0$
RECALL:
The Zero-Factor Property states that if $ab=0$, then $a=0$ or $b=0$, or both are zero.
Use the Zero-Factor Property by equating each factor to zero to obtain:
$5x=0$ or $x+4=0$
Solve each equation to obtain:
$5x=0
\\\frac{5x}{5}=\frac{0}{5}
\\x=0$
or
$x+4=0
\\x=0-4
\\x=-4$
Therefore, the solution set is $\color{blue}{\left\{-4, 0\right\}}$.