Solve y=3(2x+1)(2-x)

$$y = 3 ( 2 x + 1 ) ( 2 - x )$$

Solve for y

$$y=-3\left(x-2\right)\left(2x+1\right)$$

Solution Steps

Use the distributive property to multiply 3 by 2x+1.

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

Use the distributive property to multiply 6x+3 by 2-x and combine like terms.

$$y=9x-6x^{2}+6$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{225-24y}}{12}+\frac{3}{4}$$

$$x=\frac{\sqrt{225-24y}}{12}+\frac{3}{4}$$

Solve for x

$$x=-\frac{\sqrt{225-24y}}{12}+\frac{3}{4}$$

$$x=\frac{\sqrt{225-24y}}{12}+\frac{3}{4}\text{, }y\leq \frac{75}{8}$$