#### Answer

$\color{blue}{\left\{-\frac{6}{5}, -1, 0\right\}}$

#### Work Step by Step

RECALL:
Zero-Factor Property:
If $ab = 0$, then either $a=0$ or $b=0$ or both are $0$.
Use the property above to obtain:
\begin{array}{ccccc}
&x=0 &\text{or} &x+1=0 &\text{or} &5x+6=0
\end{array}
Solve each equation to obtain:
$x=0$
or
$x+1=0
\\x=0-1
\\x=-1$
or
$5x+6=0
\\5x=0-6
\\5x=-6
\\\frac{5x}{5}=\frac{-6}{5}
\\x=-\frac{6}{5}$
Thus, the solution set is $\color{blue}{\left\{-\frac{6}{5}, -1, 0\right\}}$.