Acquisition method, Equity composition

During acquisition method we are combining A, L, Rev. and exp.

What happens to Equity if we bought the company with cash?

During stock offer I know, we would increase capital stock by the amount and increase by minority stake, so A+L=E

but what is Equity during cash offer?

Cash is reduced and Investment is created and then consolidate?

For Equity (under cash offer), common stock and RE of acquirer remain the same. Cash (asset) is reduced.