Give the species and their constants and the system is solved as it stands — no approximation about which term dominates, and no assumption that one equilibrium can be treated apart from the others.
The same solver is behind every page here: the pH of any mixture, a titration curve point by point, the speciation of a polyprotic acid or a complex, and the solubility a Ksp allows.
Chemical equilibrium, solved exactly and drawn in your browser. The tools need JavaScript; these are the pages they offer: