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]
(..) I don’t think the boy can handle it. I don’t trust him. With all due respect, Master, is he not the chosen one? Is he not to destroy the Sith and bring balance to the Force? So the prophecy says. YODA: A prophecy that misread could have been. He will not let me down. He never has. (..)2005 Star Wars: Episode III - Revenge of the Sith
(..) Well, the mirror looks like it's reflecting something. Yeah, the closet where the blackmailer took the video from. Now I'm gonna amp up the color balance and brighten the pixelation. Now, unfortunately, you still can't make out the face. No. (..)2016 TvShow: Bones Title: The Fight in the Fixer Season: 11 Episode 15
(..) Oh, God! You think you're saving anyone? I am Thor, son of Odin, and as long as there is life in my breast, I am...running out of things to say! Are you ready? It's terribly well balanced. Well, if there's too much weight, you lose power on the swing, so. I got it! Create a heat seal. I can... (..)2015 Avengers: Age of Ultron