beat (your) brains out

to spend a lot of time worrying about a problem and thinking about how to deal with it.

I've been beating my brains out trying to think of a way of getting the money to her in time. (often + doing something)

• give a fig
• give a foot in the door
• give a free hand
• give a free reign
• give a free rein
• give a hand
• give a hard time
• give a head start
• give a heads up
• give a hoot
• give a hostage to fortune
• give a leg up
• give a lick and a promise
• give all
• give [a lot of/some etc.] stick
• give a lot of stick
• give a miss
• give a monkey's
• give-and-take
• give and take
• give an earful
• give an even break
• give a new lease of life
• give an inch
• Give an inch and take a mile.