Answer
$x=-\displaystyle \frac{1}{3}$
Work Step by Step
Recognize powers of 3
$((3^{4})^{x-2})((3^{3})^{x+1})=(3^{2})^{2x-3} \quad$ ... apply $(a^{m})^{n}a^{mn}$
$ 3^{4x-8}\cdot 3^{3x+3}=3^{4x-6} \quad$ ... apply $a^{m}a^{n}=a^{mn}$
$3^{4x-8+3x+3}=3^{4x-6}$
$ 3^{7x-5}=3^{4x-6}\qquad$ ... apply the exponential equality principle
$7x-5=4x-6$
$3x=-1$
$x=-\displaystyle \frac{1}{3}$
