We study the thermal variations of the ferromagnetic spin-3/2 Blume-Emery-Griffiths(BEG) model with repulsive biquadratic coupling by using the lowest approximation of the cluster variation method (LACVM) in the absence and presence of the external magnetic field. We obtain metastable and unstable branches of the order parameters besides the stable branches and phase transitions of these branches are investigated extensively. The classification of the stable, metastable and unstable states is made by comparing the free energy values of these states. We also study the dynamics of the model by using the path probability method (PPM) with the point distribution in order to make sure that we find and define the metastable and unstable branches of the order parameters completely and correctly. We present the metastable phase diagrams in addition to the equilibrium phase diagrams in the (kT/J, K/J) and (kT/J, D/J) planes. It is found that the metastable phase diagrams always exist at the low temperatures, which are consistent with experimental and theoretical works. (C) 2007 Elsevier B.V. All rights reserved.