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

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

Solve for N

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

Solution Steps

Use the distributive property to multiply -2y+3 by 1-y and combine like terms.

$$N=-5y+2y^{2}+3$$

Solve for y (complex solution)

$$y=\frac{-\sqrt{8N+1}+5}{4}$$

$$y=\frac{\sqrt{8N+1}+5}{4}$$

Solve for y

$$y=\frac{-\sqrt{8N+1}+5}{4}$$

$$y=\frac{\sqrt{8N+1}+5}{4}\text{, }N\geq -\frac{1}{8}$$