The collective modes that are the collective excitations in the hot QCD medium produced in the heavy-ion collision experiments have been studied. These modes being real or imaginary and stable or unstable affect the evolution of the medium. To go into the more profound analysis we incorporated several aspects of the medium such as anisotropy, the presence of medium particle collisions, and finite baryonic chemical potential. The first two facets have been studied several times from different perspectives but the inclusion of finite chemical potential is a missing part. Therefore, to have a close analysis, we have combined these effects. The medium particle collision has been included using BGK-collisional kernel, the anisotropy, and finite chemical potential enter via quarks, anti-quarks and gluons distribution functions. Our results indicate that the presence of finite chemical potential enhances the magnitude of unstable modes which may affect the fast thermalization of the hot QCD medium. Moreover, it is interesting to see the consequences of finite chemical potential along with the other aspects of the created medium from the viewpoint of low-energy heavy-ion collision experiments that operate at low temperatures and finite baryon density.