Answer
$x\in\{-1,4\}$
Work Step by Step
On the LHS, apply $a^{m}\cdot a^{n}=a^{m+n}.$
On the RHS, recognize $81$ as $3^{4}$
$ 3^{3x+x^{2}}=3^{4}\qquad$ ... apply the exponential equality principle
$3x+x^{2}=4$
$x^{2}+3x-4=0$
$(x+1)(x-4)=0$
$x=-1, x=4$
