Solve h=1/2gt^2+Vt

$$h = \frac { 1 } { 2 } g t ^ { 2 } + V t$$

Solve for V

$$\left\{\begin{matrix}V=-\frac{gt}{2}+\frac{h}{t}\text{, }&t\neq 0\\V\in \mathrm{R}\text{, }&h=0\text{ and }t=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$\frac{1}{2}gt^{2}+Vt=h$$

Subtract \frac{1}{2}gt^{2} from both sides.

$$Vt=h-\frac{1}{2}gt^{2}$$

The equation is in standard form.

$$tV=-\frac{gt^{2}}{2}+h$$

Divide both sides by t.

$$\frac{tV}{t}=\frac{-\frac{gt^{2}}{2}+h}{t}$$

Dividing by t undoes the multiplication by t.

$$V=\frac{-\frac{gt^{2}}{2}+h}{t}$$

Divide h-\frac{gt^{2}}{2} by t.

$$V=-\frac{gt}{2}+\frac{h}{t}$$

Solve for g

$$\left\{\begin{matrix}g=-\frac{2\left(Vt-h\right)}{t^{2}}\text{, }&t\neq 0\\g\in \mathrm{R}\text{, }&h=0\text{ and }t=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$\frac{1}{2}gt^{2}+Vt=h$$

Subtract Vt from both sides.

$$\frac{1}{2}gt^{2}=h-Vt$$

The equation is in standard form.

$$\frac{t^{2}}{2}g=h-Vt$$

Divide both sides by \frac{1}{2}t^{2}.

$$\frac{2\times \frac{t^{2}}{2}g}{t^{2}}=\frac{2\left(h-Vt\right)}{t^{2}}$$

Dividing by \frac{1}{2}t^{2} undoes the multiplication by \frac{1}{2}t^{2}.

$$g=\frac{2\left(h-Vt\right)}{t^{2}}$$