Solve y=(x-30)(-2x+100)

$$y = ( x - 30 ) ( - 2 x + 100 )$$

Solve for y

$$y=2\left(50-x\right)\left(x-30\right)$$

Solution Steps

Use the distributive property to multiply x-30 by -2x+100 and combine like terms.

$$y=-2x^{2}+160x-3000$$

Solve for x (complex solution)

$$x=\frac{\sqrt{400-2y}}{2}+40$$

$$x=-\frac{\sqrt{400-2y}}{2}+40$$

Solve for x

$$x=\frac{\sqrt{400-2y}}{2}+40$$

$$x=-\frac{\sqrt{400-2y}}{2}+40\text{, }y\leq 200$$