Graph + number of solutions problem

I've been working through a problem and once again seem to be stuck and in need of all your erudite support, if anyone's available!

I first had to sketch y = x^2*e^-x, which was easy enough investigating the intercept, considering limits and looking at first and second derivatives. I've checked my answer against a graphical calculator so know that I'm not overcomplicating the follow-up by getting this wrong!

What's stumping me is the next part:

A > 0
x^2*e^-x = A(1+x) has TWO solutions
What is the larger solution?

I've tried a few scenarios graphically, but the problem is it seems to me that there are multiple values of m that will work (in fact surely any value below a certain critical value somewhere about 0.4 by my very crude estimations). So I assume that I need to express it in terms of A. I've thought long and hard about it but I really can't seem to derive any equations to work with so any help would be great!

Thanks very much in advance.