The other day, I came across the problem (or something that reduced to the problem):
Solve for $x$ in terms of $y$ and $e$: $$x^2e^x=y$$
I tried for a while to solve it with logarithms, roots, and the like, but simply couldn't get $x$ onto one side by itself without having $x$ on the other side too.
So, how can I solve this, step-by-step?
More generally, how can I solve equations that involve both polynomials (e.g. $x^2$, $x^3$) and exponentials (e.g. $e^x$,$10^x$)?
EDIT - I now remember why I this question came up. I was reading something about complexity theory (the basics: P, NP, NP-hard, etc.), and I got to a part that talked about how polynomial time is more efficient than exponential time. So, I decided to take a very large polynomial function and a very small exponential function and see where they met. Hence, I had to solve an equation with both polynomials and exponentials, which I figured could reduce to $x^2e^x=y$.