Solve xleft(-1/2+2xright)=left(x-3/2right)left(2x+4right)

$$x \left( - \frac{ 1 }{ 2 } +2x \right) = \left( x- \frac{ 3 }{ 2 } \right) \left( 2x+4 \right)$$

Evaluate

$$\left(2x-3\right)\left(x+2\right)$$

Solution Steps

Apply the distributive property by multiplying each term of x-\frac{3}{2} by each term of 2x+4.

$$2x^{2}+4x-\frac{3}{2}\times 2x-\frac{3}{2}\times 4$$

Cancel out 2 and 2.

$$2x^{2}+4x-3x-\frac{3}{2}\times 4$$

Combine 4x and -3x to get x.

$$2x^{2}+x-\frac{3}{2}\times 4$$

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

$$2x^{2}+x+\frac{-3\times 4}{2}$$

Multiply -3 and 4 to get -12.

$$2x^{2}+x+\frac{-12}{2}$$

Divide -12 by 2 to get -6.

$$2x^{2}+x-6$$

Expand

$$2x^{2}+x-6$$

Solution Steps

Apply the distributive property by multiplying each term of x-\frac{3}{2} by each term of 2x+4.

$$2x^{2}+4x-\frac{3}{2}\times 2x-\frac{3}{2}\times 4$$

Cancel out 2 and 2.

$$2x^{2}+4x-3x-\frac{3}{2}\times 4$$

Combine 4x and -3x to get x.

$$2x^{2}+x-\frac{3}{2}\times 4$$

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

$$2x^{2}+x+\frac{-3\times 4}{2}$$

Multiply -3 and 4 to get -12.

$$2x^{2}+x+\frac{-12}{2}$$

Divide -12 by 2 to get -6.

$$2x^{2}+x-6$$