Answer
$x=-\displaystyle \frac{2}{5}$
Work Step by Step
We want to use the principle of exponential equality,
$b^{m}=b^{n}$ is equivalent to $m=n$,
but the bases are not equal.
So, we rewrite $9$ as $3^{2}$ and $27$ as $3^{3}$
$(3^{2})^{x+1}=(3^{3})^{-x}\qquad$ ... apply $(a^{m})^{n}=a^{mn}$
$3^{2(x+1)}=3^{-3x}$
... and now, we apply the principle of exponential equality,
$ 2x+2=-3x\qquad$... add $3x-2$
$5x=-2$
$x=-\displaystyle \frac{2}{5}$
