The phrase "reach an equilibrium" indicates a state of balance and stability. There are several synonyms that can be used to convey the same meaning. The phrase "attain a balance" suggests that a state of equilibrium has been achieved after making several adjustments. "Reach a steady state" implies a settled condition, often after a period of change. "Establish an even distribution" can be used when referring to material or resources being distributed equally. "Maintain a stable equilibrium" suggests the state of balance has been achieved and must be preserved. Whatever synonym is chosen, the underlying idea remains the same, which is to indicate a harmonious and stable outcome.