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!