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]
(..) He will do whatever he must to win. (URGING HORSES) Now, when you cut first, they'll tend to put you up on one wheel. So, you have to learn how to tilt. It's all about balance, Judah. It's a dangerous maneuver, of course, but with courage and practice, it can be mastered. This is the spina. (..)2016 Ben-Hur
(..) I know when I found you, you were almost dead. And for what? So you can say you evened up with the Romans? We're not trying to balance anything. We want the freedom we were born with. And if the Romans won't give it to us, we'll have to take it by force. How many Romans do you even know? (..)2016 Ben-Hur