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 may not fit in here. Maybe you can shift the integrator unit further up into the cavity. l'll try it. Balance servo again? Yeah, she fell over this afternoon. l think it's the sensor. lf it's the central unit we'll open her up. You get a confirmation before you do that. What's he in for? (..)1973 Westworld
(..) That's amazing! Supposedly, you really can't tell... except by looking at the hands. They haven't perfected the hands yet. l have a quick fade on the CRT and my balance controls don't seem to help me. l'm keeping this in real time. Switch me over to an on-line status and l'll do it manually. (..)1973 Westworld