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]
(..) ...because I want some kind of protection or amnesty. I had nothing to do with the Bailey and made a mistake in the Jordan Tower. - I think this should balance it out. - What are you talking about? I'm Evey Hammond. I'm... I've been the prisoner of the terrorist V for the past several weeks. (..)2005 V for Vendetta