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-4x^{2}+4x+9-\left(6x+3\right)
Combine 2x^{2} and -6x^{2} to get -4x^{2}.
-4x^{2}+4x+9-6x-3
To find the opposite of 6x+3, find the opposite of each term.
-4x^{2}-2x+9-3
Combine 4x and -6x to get -2x.
-4x^{2}-2x+6
Subtract 3 from 9 to get 6.
-4x^{2}+4x+9-\left(6x+3\right)
Combine 2x^{2} and -6x^{2} to get -4x^{2}.
-4x^{2}+4x+9-6x-3
To find the opposite of 6x+3, find the opposite of each term.
-4x^{2}-2x+9-3
Combine 4x and -6x to get -2x.
-4x^{2}-2x+6
Subtract 3 from 9 to get 6.