I am told to maximize the area of a rectangular area within the graph

$\displaystyle y=3e^{-8x^2+2}$

And the area equation I came up with is $\displaystyle A=2xy$

I understand optimization problems just fine and I know the above equations are correct, I'm just having a lot of trouble simplifying my answer. If anyone cares to take a look at it, that'd be swell.