Solve y=24-(6-t)2t

$$y = 24 - ( 6 - t ) 2 t$$

Solve for y

$$y=2\left(t^{2}-6t+12\right)$$

Solution Steps

Use the distributive property to multiply 6-t by 2.

$$y=24-\left(12-2t\right)t$$

Use the distributive property to multiply 12-2t by t.

$$y=24-\left(12t-2t^{2}\right)$$

To find the opposite of 12t-2t^{2}, find the opposite of each term.

$$y=24-12t+2t^{2}$$

Solve for t (complex solution)

$$t=-\frac{\sqrt{2y-12}}{2}+3$$

$$t=\frac{\sqrt{2y-12}}{2}+3$$

Solve for t

$$t=-\frac{\sqrt{2y-12}}{2}+3$$

$$t=\frac{\sqrt{2y-12}}{2}+3\text{, }y\geq 6$$