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]
(..) A female with young makes an easier target. Her large paws give an excellent grip and that long tail helps her balance. Silently she positions herself above her prey. She returns with nothing. Golden eagles patrol these cliffs in search of the weak or injured. (..)2006 TvShow: Planet Earth Title: Mountains Season: 1 Episode 2