He's trying to keep his work life and his family life 'in balance'. = He's trying to keep his work life 'in balance with' his family life. [=he's trying to give a proper of amount of time and attention to both his work life and his family life]
The discount 'balances out' the shipping charge. = The discount and the shipping charge 'balance' each other 'out'. [=the shipping charge and the discount together equal zero]
He needs to achieve/create/strike a better 'balance' between his work life and his family life. [=he needs to spend less time at work and more time with his family]
(..) with the capitol's children? You're joking? Not in the slightest. Is this Plutarch's idea? It was mine. It balances the need for revenge with the least loss of human life. - You may cast your votes. - No. No, obviously not. (..)2015 The Hunger Games: Mockingjay - Part 2