Math question

I saw this math problem some time ago and I was never able to figure the problem out.  Here it is:
\begin{equation}
\frac{3x^2}{9^x} = 27
\end{equation}
I was able to obtain the following steps:
\begin{equation}
\frac{3x^2}{3^{2x}} = 3^3
\end{equation}
\begin{equation}
3x^2 = 3^{2x+3}
\end{equation}
\begin{equation}
x^2 = 3^{2(x+1)}
\end{equation}
This is where I get lost and can't solve it without a CAS or knowing that the answer is -1.  I hope someone can show and explain how to solve it the "pencil and paper" way.

Testing LATEX

I'm just trying to test out LaTeX on Blogger.
\begin{equation}
\int x dx = \frac{1}{2}x^2 + C
\end{equation}
Hooray, it works!