Evaluate
4x^{3}-12x^{2}+16x-\frac{65}{4}
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4x^{3}-12x^{2}+16x-\frac{65}{4}
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\left(2x^{2}-3x+\frac{6+1}{2}\right)\left(2x-3\right)-\frac{5\times 4+3}{4}
Multiply 3 and 2 to get 6.
\left(2x^{2}-3x+\frac{7}{2}\right)\left(2x-3\right)-\frac{5\times 4+3}{4}
Add 6 and 1 to get 7.
\left(2x^{2}-3x+\frac{7}{2}\right)\left(2x-3\right)-\frac{20+3}{4}
Multiply 5 and 4 to get 20.
\left(2x^{2}-3x+\frac{7}{2}\right)\left(2x-3\right)-\frac{23}{4}
Add 20 and 3 to get 23.
4x^{3}-12x^{2}+16x-\frac{21}{2}-\frac{23}{4}
Use the distributive property to multiply 2x^{2}-3x+\frac{7}{2} by 2x-3 and combine like terms.
4x^{3}-12x^{2}+16x-\frac{65}{4}
Subtract \frac{23}{4} from -\frac{21}{2} to get -\frac{65}{4}.
\left(2x^{2}-3x+\frac{6+1}{2}\right)\left(2x-3\right)-\frac{5\times 4+3}{4}
Multiply 3 and 2 to get 6.
\left(2x^{2}-3x+\frac{7}{2}\right)\left(2x-3\right)-\frac{5\times 4+3}{4}
Add 6 and 1 to get 7.
\left(2x^{2}-3x+\frac{7}{2}\right)\left(2x-3\right)-\frac{20+3}{4}
Multiply 5 and 4 to get 20.
\left(2x^{2}-3x+\frac{7}{2}\right)\left(2x-3\right)-\frac{23}{4}
Add 20 and 3 to get 23.
4x^{3}-12x^{2}+16x-\frac{21}{2}-\frac{23}{4}
Use the distributive property to multiply 2x^{2}-3x+\frac{7}{2} by 2x-3 and combine like terms.
4x^{3}-12x^{2}+16x-\frac{65}{4}
Subtract \frac{23}{4} from -\frac{21}{2} to get -\frac{65}{4}.
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