Answer
$x=\frac{-3}{2}$
Work Step by Step
We rewrite both sides, so that the base is $e$ on both sides.
$e^{3-x}=(e^3)^{-x}$
By the law of exponents: $(a^x)^y=a^{xy}$
$(e^3)^{-x}=e^{-3x}$
The rewritten equation:
$e^{3-x}=e^{-3x}$
Then, since the base of both sides are the same, we set the exponents equal, because the two sides are equal only if the powers are equal too:
$3-x=-3x$
$2x=-3$
$x=\frac{-3}{2}$