Answer
$\color{blue}{\left\{-\frac{5}{7}, 0, \frac{8}{3}, 6\right\}}$.
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}
&4.5w=0 &\text{or} &3w-8=0 &\text{or} &7w+5=0 &\text{or} &w-6=0
\end{array}
Solve each equation to obtain:
$4.5w=0
\\\frac{4.5w}{4.5}=\frac{0}{4.5}
\\w=0$
or
$3w-8=0
\\3w=8
\\\frac{3w}{3}=\frac{8}{3}
\\w=\frac{8}{3}$
or
$7w+5=0
\\7w=-5
\\\frac{7w}{7}=\frac{-5}{7}
\\w=-\frac{5}{7}$
or
$w-6=0
\\w=0+6
\\w=6$
Thus, the solution set is $\color{blue}{\left\{-\frac{5}{7}, 0, \frac{8}{3}, 6\right\}}$.
