A balancing act 的意思是左右逢源，兼顾各方。这个表达来源于马戏表演。

例句

The life of a modern parent is a balancing act of going out to work and raising children at home.

My sisters are always fighting between themselves. Keeping the peace at home is a balancing act.

请注意

To balance something against something else 的意思是对事情进行权衡比较。

During a recession a government has to balance the needs of the poorest against the wishes of the richest.