English: $- \frac{\hslash^{2}}{2m}\left\lbrack 2 + 4\alpha r + \alpha^{2}r^{2} \right\rbrack e^{- \alpha r} + \frac{2\hslash^{2}}{2mr^{2}}r^{2}e^{- \alpha r} - \frac{Ze^{2}}{4\pi\epsilon_{0}}re^{- \alpha r} = Er^{2}e^{- \alpha r}$ Equate the terms with power r and I get and this gives me the energy.
Telugu: $- \frac{\hslash^{2}}{2m}\లెఫ్ట్\lbrack 2 + 4\alpha r + \alpha^{2}r^{2} \right\rbrack e^{- \alpha r} + \frac{2\hslash^{2}}{2mr^{2}}r^{2}e^{- \alpha r} - \frac{Ze^{2}}{4\pi epsilon_{0}\alpha r} = Er^{2}e^{- \alpha r}