Solve v_{F}=v_{0}-gt

$$v _ { F } = v _ { 0 } - g t$$

Solve for g

$$\left\{\begin{matrix}g=\frac{v_{0}-v_{F}}{t}\text{, }&t\neq 0\\g\in \mathrm{R}\text{, }&v_{F}=v_{0}\text{ and }t=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$v_{0}-gt=v_{F}$$

Subtract v_{0} from both sides.

$$-gt=v_{F}-v_{0}$$

The equation is in standard form.

$$\left(-t\right)g=v_{F}-v_{0}$$

Divide both sides by -t.

$$\frac{\left(-t\right)g}{-t}=\frac{v_{F}-v_{0}}{-t}$$

Dividing by -t undoes the multiplication by -t.

$$g=\frac{v_{F}-v_{0}}{-t}$$

Divide v_{F}-v_{0} by -t.

$$g=-\frac{v_{F}-v_{0}}{t}$$

Solve for t

$$\left\{\begin{matrix}t=\frac{v_{0}-v_{F}}{g}\text{, }&g\neq 0\\t\in \mathrm{R}\text{, }&v_{F}=v_{0}\text{ and }g=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$v_{0}-gt=v_{F}$$

Subtract v_{0} from both sides.

$$-gt=v_{F}-v_{0}$$

The equation is in standard form.

$$\left(-g\right)t=v_{F}-v_{0}$$

Divide both sides by -g.

$$\frac{\left(-g\right)t}{-g}=\frac{v_{F}-v_{0}}{-g}$$

Dividing by -g undoes the multiplication by -g.

$$t=\frac{v_{F}-v_{0}}{-g}$$

Divide v_{F}-v_{0} by -g.

$$t=-\frac{v_{F}-v_{0}}{g}$$