The paper proposes a linear algebraic based approach to finding a set of home markings in a bounded and live Equal Conflict System. Our algorithm is based on the theory of T-invariants, controlled-siphons and traps. The idea is to decompose the initial net in a certain subset of T-components, which are Choice-Free nets, find a set of live and potentially reversible markings for them and then compose these markings along the set of shared places. We also prove that the algorithm has NP complexity.