when you are trying to please two or more people or groups who all want different things, or who have ideas that are completely different from each other:
Gilmore had to perform the difficult balancing act of attracting moderate voters without losing his conservative base.
Definition from the Longman Dictionary of Contemporary English Advanced Learner's Dictionary.
Dictionary pictures of the day
Do you know what each of these is called?
Click on any of the pictures above to find out what it is called.