Solve (3x+2)(-3/2x+1)

$$( 3 x + 2 ) ( - \frac { 3 } { 2 } x + 1 )$$

Evaluate

$$-\frac{9x^{2}}{2}+2$$

Solution Steps

Apply the distributive property by multiplying each term of 3x+2 by each term of -\frac{3}{2}x+1.

$$3x\left(-\frac{3}{2}\right)x+3x+2\left(-\frac{3}{2}\right)x+2$$

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

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

Express 3\left(-\frac{3}{2}\right) as a single fraction.

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

Multiply 3 and -3 to get -9.

$$\frac{-9}{2}x^{2}+3x+2\left(-\frac{3}{2}\right)x+2$$

Fraction \frac{-9}{2} can be rewritten as -\frac{9}{2} by extracting the negative sign.

$$-\frac{9}{2}x^{2}+3x+2\left(-\frac{3}{2}\right)x+2$$

Cancel out 2 and 2.

$$-\frac{9}{2}x^{2}+3x-3x+2$$

Combine 3x and -3x to get 0.

$$-\frac{9}{2}x^{2}+2$$

Expand

$$-\frac{9x^{2}}{2}+2$$

Solution Steps

Apply the distributive property by multiplying each term of 3x+2 by each term of -\frac{3}{2}x+1.

$$3x\left(-\frac{3}{2}\right)x+3x+2\left(-\frac{3}{2}\right)x+2$$

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

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

Express 3\left(-\frac{3}{2}\right) as a single fraction.

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

Multiply 3 and -3 to get -9.

$$\frac{-9}{2}x^{2}+3x+2\left(-\frac{3}{2}\right)x+2$$

Fraction \frac{-9}{2} can be rewritten as -\frac{9}{2} by extracting the negative sign.

$$-\frac{9}{2}x^{2}+3x+2\left(-\frac{3}{2}\right)x+2$$

Cancel out 2 and 2.

$$-\frac{9}{2}x^{2}+3x-3x+2$$

Combine 3x and -3x to get 0.

$$-\frac{9}{2}x^{2}+2$$