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]
(..) Look, you chose me for something. I will stand and fight. You know I will. But I need a little help here. Our Great Mother does not take sides, Jake. She protects only the balance of life. It was worth a try. Yeah! Yeah! That's what I'm talking about! Yeah! Yeah! That's what I'm talking about, man! (..)2009 Avatar