Population balances for simultaneous coagulation and breakage (and their analogs, e.g., polymerization and depolymerization) are employed in describing many systems (e.g., aerosols, powders and polymers), and many unit operations including reactors, crystallizers and size reduction/enlargement equipment. The population balance equations for homogeneous coagulation rate, power-law breakage rate and self-similar daughter particles are solved in moment form under a polynomial interpolative closure rule. Limiting steady-state analytical approximations for the distribution function of the very small particles are incorporated into basis sets enabling reconstruction of the distributions from their moments utilizing a nonlinear regression technique.