E radial equation for a hydrogenic atom

[ElectricEel1]

Homework Statement

By substituting R(r)=r^2*e^(-r/a) into the radial equation for a hydrogenic atom, find the values of a, ℓ and E for which the function R(r).

Homework Equations

http://puu.sh/rOJQ3/8bcad54c45.png

The Attempt at a Solution

I took the first derivative of R(r), then multiplied it by r^2 before taking the derivative again to get

e^(-r/a)*(r^4/a - 6r^3/a + 6r^2)
then when putting it back into the radial equation ended with

-h^c/m * e^-r/a (r^2/(2a^2) - 3r/a + 3) + (h^2l(l+1))/2m) e^-r/a - (ze^2)/(4pi*epsilon_0)*r*e^(-r/a) = E*R(r)

then dividing by R(r) = r^2*e^(-r/a) i got

-h^2*c/(mr^2) (r^2/2a^2 - 3r/a + 3) + h^2l(l+1)/2mr^2 - ze^2/4pi*ep_0 = E

I don't really know where to go next with this to find E,a, and L.

thanks

 

[ElectricEel1]

bump