Based on the fact that the Hamiltonians of the Coulomb many-particle systems are always factorized we develop the two different approaches for analytical solution of the Schrodinger equation written for arbitrary few- and many-particle Coulomb systems. The first approach is the matrix factorization method. Another method is based on the D+-series of representations of the hyper-radial 0(2,1)-algebra. The both these methods allow us to obtain the closed analytical formulas for the bound state energies in an arbitrary many-particle Coulomb system.