A simplified double-exchange model is suggested being the s-d model in the strong coupling limit with neglecting transverse localized spins fluctuations. Dynamical mean-field approximation is used, where localized spins are treated as quantum values in contrast to the previous approaches. The simplification allows on the Bethe lattice to derive analytically equations for both electronic and localized spins averages. Magnetic phase diagram including a phase separation region was calculated on the temperature-electron concentration plane. The wide set of calculated properties of the model is consistent with experimental data for the CMR-manganites.