# How to solve for the equation $ax \exp(bx)=c$?

How to solve for the equation $ax \exp(bx)=c$? It is known that $x\geq 0$.

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In general, we can rewrite the equation as $(bx) \exp(bx) = \frac{bc}{a} = d$ (say). The solution for this is $bx = W(d)$, or $x = \frac{1}{b}W(d)$. –  Srivatsan Nov 23 '11 at 22:55