Solve y=3(x-6)(x-4)/2

$$y = \frac { 3 ( x - 6 ) ( x - 4 ) } { 2 }$$

Solve for y

$$y=\frac{3\left(x-6\right)\left(x-4\right)}{2}$$

Solution Steps

Use the distributive property to multiply 3 by x-6.

$$y=\frac{\left(3x-18\right)\left(x-4\right)}{2}$$

Use the distributive property to multiply 3x-18 by x-4 and combine like terms.

$$y=\frac{3x^{2}-30x+72}{2}$$

Divide each term of 3x^{2}-30x+72 by 2 to get \frac{3}{2}x^{2}-15x+36.

$$y=\frac{3}{2}x^{2}-15x+36$$

Solve for x (complex solution)

$$x=\frac{\sqrt{6y+9}}{3}+5$$

$$x=-\frac{\sqrt{6y+9}}{3}+5$$

Solve for x

$$x=\frac{\sqrt{6y+9}}{3}+5$$

$$x=-\frac{\sqrt{6y+9}}{3}+5\text{, }y\geq -\frac{3}{2}$$