The search for the conjectured QCD critical point is being conducted experimentally at large baryon densities. Theoretical simulations of these experiments require the explicit inclusion of finite baryon (B), strangeness (S), and electric charge density (Q). We derive the hydrodynamic equations of motion of an out-of-equilibrium multi-charged fluid of strongly interacting QCD matter. Our set of equations incorporates, up to second order, dissipative (shear and bulk viscosities) and BSQ diffusive currents as well as all coupling terms. I will present the stability analysis which examines the response of our system of equations to linear perturbations and evaluate the set of conditions under which these equations are hydrodynamically and thermodynamically stable.