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8-\left(5-4\left(-6+7\times 3\right)-3\right)
Subtract 2 from 5 to get 3.
8-\left(5-4\left(-6+21\right)-3\right)
Multiply 7 and 3 to get 21.
8-\left(5-4\times 15-3\right)
Add -6 and 21 to get 15.
8-\left(5-60-3\right)
Multiply 4 and 15 to get 60.
8-\left(-55-3\right)
Subtract 60 from 5 to get -55.
8-\left(-58\right)
Subtract 3 from -55 to get -58.
8+58
The opposite of -58 is 58.
66
Add 8 and 58 to get 66.