The expression TO BEND OVER BACKWARD means to make a great effort to help sb or to reach agreement with sb:
He has bent over backward to please her, but she’s been unsatisfied all the time.
I’ll bend over backward to make the deal with them.
You’ll have to bend over backward to show that you really care.
She would bend over backward for her husband.
There are some other versions of this expressions, with the same meaning, like LEAN OVER BACKWARD or FALL OVER BACKWARD:
I’ve leaned over backward to help you and you haven’t even said thank you.
If we are to work together, we will both have to lean over backward to reach a compromise sometimes.
He has to fall over backward to make her happy.
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