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\left(2x^{2}-3x+12x-18\right)\left(x-6\right)
Apply the distributive property by multiplying each term of x+6 by each term of 2x-3.
\left(2x^{2}+9x-18\right)\left(x-6\right)
Combine -3x and 12x to get 9x.
2x^{3}-12x^{2}+9x^{2}-54x-18x+108
Apply the distributive property by multiplying each term of 2x^{2}+9x-18 by each term of x-6.
2x^{3}-3x^{2}-54x-18x+108
Combine -12x^{2} and 9x^{2} to get -3x^{2}.
2x^{3}-3x^{2}-72x+108
Combine -54x and -18x to get -72x.
\left(2x^{2}-3x+12x-18\right)\left(x-6\right)
Apply the distributive property by multiplying each term of x+6 by each term of 2x-3.
\left(2x^{2}+9x-18\right)\left(x-6\right)
Combine -3x and 12x to get 9x.
2x^{3}-12x^{2}+9x^{2}-54x-18x+108
Apply the distributive property by multiplying each term of 2x^{2}+9x-18 by each term of x-6.
2x^{3}-3x^{2}-54x-18x+108
Combine -12x^{2} and 9x^{2} to get -3x^{2}.
2x^{3}-3x^{2}-72x+108
Combine -54x and -18x to get -72x.