Solve -4x(3/2x-5)-(3/2x-5)

$$- 4 x ( \frac { 3 } { 2 } x - 5 ) - ( \frac { 3 } { 2 } x - 5 )$$

Evaluate

$$-6x^{2}+\frac{37x}{2}+5$$

Solution Steps

Use the distributive property to multiply -4x by \frac{3}{2}x-5.

$$-4x\times \frac{3}{2}x+20x-\left(\frac{3}{2}x-5\right)$$

Multiply x and x to get x^{2}.

$$-4x^{2}\times \frac{3}{2}+20x-\left(\frac{3}{2}x-5\right)$$

Express -4\times \frac{3}{2} as a single fraction.

$$\frac{-4\times 3}{2}x^{2}+20x-\left(\frac{3}{2}x-5\right)$$

Multiply -4 and 3 to get -12.

$$\frac{-12}{2}x^{2}+20x-\left(\frac{3}{2}x-5\right)$$

Divide -12 by 2 to get -6.

$$-6x^{2}+20x-\left(\frac{3}{2}x-5\right)$$

To find the opposite of \frac{3}{2}x-5, find the opposite of each term.

$$-6x^{2}+20x-\frac{3}{2}x-\left(-5\right)$$

The opposite of -5 is 5.

$$-6x^{2}+20x-\frac{3}{2}x+5$$

Combine 20x and -\frac{3}{2}x to get \frac{37}{2}x.

$$-6x^{2}+\frac{37}{2}x+5$$

Expand

$$-6x^{2}+\frac{37x}{2}+5$$

Solution Steps

Use the distributive property to multiply -4x by \frac{3}{2}x-5.

$$-4x\times \frac{3}{2}x+20x-\left(\frac{3}{2}x-5\right)$$

Multiply x and x to get x^{2}.

$$-4x^{2}\times \frac{3}{2}+20x-\left(\frac{3}{2}x-5\right)$$

Express -4\times \frac{3}{2} as a single fraction.

$$\frac{-4\times 3}{2}x^{2}+20x-\left(\frac{3}{2}x-5\right)$$

Multiply -4 and 3 to get -12.

$$\frac{-12}{2}x^{2}+20x-\left(\frac{3}{2}x-5\right)$$

Divide -12 by 2 to get -6.

$$-6x^{2}+20x-\left(\frac{3}{2}x-5\right)$$

To find the opposite of \frac{3}{2}x-5, find the opposite of each term.

$$-6x^{2}+20x-\frac{3}{2}x-\left(-5\right)$$

The opposite of -5 is 5.

$$-6x^{2}+20x-\frac{3}{2}x+5$$

Combine 20x and -\frac{3}{2}x to get \frac{37}{2}x.

$$-6x^{2}+\frac{37}{2}x+5$$