Answer
$x=6$.
Work Step by Step
$9^{-x+15}=(3^2)^{-x+15}=3^{-2x+30}$, $27^x=(3^3)^x=3^{3x}$ hence the equation becomes: \begin{align*}3^{-2x+30}=3^{3x}.\end{align*}
The base is same on the 2 sides on the equation (and it is not $1$ or $-1$), hence they will be equal if the exponents are equal. Hence $-2x+30=3x\\30=5x\\x=6$.
