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]
(..) Doctor, if you have any other ideas, I am all ears. Admiral. Yes, Doctor? Godzilla may be the answer. I believe he's here to restore balance, he can defeat them. And what, we just standby and watch? I'm sorry, doctor, I can't take that risk. You'll need to prep the warheads (..)2014 Godzilla
(..) The source is the radiation, we're monitoring all known sites, - but... but if we don't find it soon... - Then what? Nature has an order, a part to restore balance. I believe he is that power. Sir, right now we're fifty miles from Hawaii. This transport will take you there. (..)2014 Godzilla