Answer
$x=3$
Work Step by Step
Rewriting $36$ as $6^{2}$ and $216$ as $6^{3}$, we have
$(6^{2})^{-3x+3}=\left( \frac{1}{6^{3}}\right)^{x+1}$
$\implies 6^{-6x+6}=6^{-3x-3}$
Equating the exponents, we get
$-6x+6=-3x-3$
$-6x+3x=-3-6$
$-3x=-9$
$\implies x=\frac{-9}{-3}=3$
Check the result:
$36^{-3(3)+3}=36^{-6}=(6^2)^{-6}=6^{-12}$
$\left(\frac{1}{216}\right)^{3+1}=\left(\frac{1}{6^3}\right)^4=6^{-12}$ which is true.
