Solve 16t^2+32t-27v=0

$$16 t ^ { 2 } + 32 t - 27 v = 0$$

Solve for v

$$v=\frac{16t\left(t+2\right)}{27}$$

Steps for Solving Linear Equation

Subtract 16t^{2} from both sides. Anything subtracted from zero gives its negation.

$$32t-27v=-16t^{2}$$

Subtract 32t from both sides.

$$-27v=-16t^{2}-32t$$

Divide both sides by -27.

$$\frac{-27v}{-27}=-\frac{16t\left(t+2\right)}{-27}$$

Dividing by -27 undoes the multiplication by -27.

$$v=-\frac{16t\left(t+2\right)}{-27}$$

Divide -16t\left(2+t\right) by -27.

$$v=\frac{16t\left(t+2\right)}{27}$$

Solve for t

$$t=\frac{\sqrt{27v+16}}{4}-1$$

$$t=-\frac{\sqrt{27v+16}}{4}-1\text{, }v\geq -\frac{16}{27}$$