Solve y=(x+2)(x-3)+2(2x-3)

$$y = ( x + 2 ) ( x - 3 ) + 2 ( 2 x - 3 )$$

Solve for y

$$y=x^{2}+3x-12$$

Solution Steps

Use the distributive property to multiply x+2 by x-3 and combine like terms.

$$y=x^{2}-x-6+2\left(2x-3\right)$$

Use the distributive property to multiply 2 by 2x-3.

$$y=x^{2}-x-6+4x-6$$

Combine -x and 4x to get 3x.

$$y=x^{2}+3x-6-6$$

Subtract 6 from -6 to get -12.

$$y=x^{2}+3x-12$$

Solve for x (complex solution)

$$x=\frac{-\sqrt{4y+57}-3}{2}$$

$$x=\frac{\sqrt{4y+57}-3}{2}$$

Solve for x

$$x=\frac{-\sqrt{4y+57}-3}{2}$$

$$x=\frac{\sqrt{4y+57}-3}{2}\text{, }y\geq -\frac{57}{4}$$