Solve y=-3(x-5)(x-6)

$$y = - 3 ( x - 5 ) ( x - 6 )$$

Solve for y

$$y=-3\left(x-6\right)\left(x-5\right)$$

Solution Steps

Use the distributive property to multiply -3 by x-5.

$$y=\left(-3x+15\right)\left(x-6\right)$$

Use the distributive property to multiply -3x+15 by x-6 and combine like terms.

$$y=-3x^{2}+33x-90$$

Solve for x (complex solution)

$$x=\frac{\sqrt{9-12y}}{6}+\frac{11}{2}$$

$$x=-\frac{\sqrt{9-12y}}{6}+\frac{11}{2}$$

Solve for x

$$x=\frac{\sqrt{9-12y}}{6}+\frac{11}{2}$$

$$x=-\frac{\sqrt{9-12y}}{6}+\frac{11}{2}\text{, }y\leq \frac{3}{4}$$