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Solve for m
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x+m=2x^{3}+9x^{2}-14x-9
Swap sides so that all variable terms are on the left hand side.
m=2x^{3}+9x^{2}-14x-9-x
Subtract x from both sides.
m=2x^{3}+9x^{2}-15x-9
Combine -14x and -x to get -15x.