Answer
The solution set is $\left\{18\right\}$.
Work Step by Step
Solve using the different properties of Algebra to find:
$-6x=-83-25
\\-6x=-108
\\x=\frac{-108}{-6}
\\x=18$
Check:
$25-6(18)\stackrel{?}{=}-83
\\25-108\stackrel{?}{=}-83
\\-83 \stackrel{\checkmark}{=}-83$
The solution set is $\left\{18\right\}$.