Solve y=12-(2-x)(x+3)

$$y = 12 - ( 2 - x ) ( x + 3 )$$

Solve for y

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

Solution Steps

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

$$y=12-\left(-x+6-x^{2}\right)$$

To find the opposite of -x+6-x^{2}, find the opposite of each term.

$$y=12+x-6+x^{2}$$

Subtract 6 from 12 to get 6.

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

Solve for x (complex solution)

$$x=\frac{-\sqrt{4y-23}-1}{2}$$

$$x=\frac{\sqrt{4y-23}-1}{2}$$

Solve for x

$$x=\frac{-\sqrt{4y-23}-1}{2}$$

$$x=\frac{\sqrt{4y-23}-1}{2}\text{, }y\geq \frac{23}{4}$$