Deriving Associated Laguerre Polynomial solutions for the Hydrogen Radial Equation

I'm currently in quantum mechanics and we are studying they hydrogen atom right now. The solutions for both the phi equation and the radial equation are expressed in associated special polynomials (associated Legendre and associated Laguerre polynomials) and I was wondering how you go about solving one of these equations (lets just go with the radial equation) from its original equation without using the known Laguerre Polynomial identities.