Solve y=4t^2+2t^2-6t

$$y = 4 { t }^{ 2 } +2 { t }^{ 2 } -6t$$

Solve for y

$$y=6t\left(t-1\right)$$

Solution Steps

Combine 4t^{2} and 2t^{2} to get 6t^{2}.

$$y=6t^{2}-6t$$

Solve for t (complex solution)

$$t=-\frac{\sqrt{6y+9}}{6}+\frac{1}{2}$$

$$t=\frac{\sqrt{6y+9}}{6}+\frac{1}{2}$$

Solve for t

$$t=-\frac{\sqrt{6y+9}}{6}+\frac{1}{2}$$

$$t=\frac{\sqrt{6y+9}}{6}+\frac{1}{2}\text{, }y\geq -\frac{3}{2}$$