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6x^{4}+15x^{2}-12x-4x\left(2x+3\right)
Use the distributive property to multiply 3x by 2x^{3}+5x-4.
6x^{4}+15x^{2}-12x-8x^{2}-12x
Use the distributive property to multiply -4x by 2x+3.
6x^{4}+7x^{2}-12x-12x
Combine 15x^{2} and -8x^{2} to get 7x^{2}.
6x^{4}+7x^{2}-24x
Combine -12x and -12x to get -24x.
6x^{4}+15x^{2}-12x-4x\left(2x+3\right)
Use the distributive property to multiply 3x by 2x^{3}+5x-4.
6x^{4}+15x^{2}-12x-8x^{2}-12x
Use the distributive property to multiply -4x by 2x+3.
6x^{4}+7x^{2}-12x-12x
Combine 15x^{2} and -8x^{2} to get 7x^{2}.
6x^{4}+7x^{2}-24x
Combine -12x and -12x to get -24x.