Solve y=h+v_{0}t-gt^2/2

$$y = h + v _ { 0 } t - \frac { g t ^ { 2 } } { 2 }$$

Solve for g (complex solution)

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

Steps for Solving Linear Equation

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

$$h+v_{0}t-\frac{gt^{2}}{2}=y$$

Subtract h from both sides.

$$v_{0}t-\frac{gt^{2}}{2}=y-h$$

Subtract v_{0}t from both sides.

$$-\frac{gt^{2}}{2}=y-h-v_{0}t$$

Multiply both sides of the equation by 2.

$$-gt^{2}=2y-2h-2v_{0}t$$

Reorder the terms.

$$-gt^{2}=2y-2tv_{0}-2h$$

The equation is in standard form.

$$\left(-t^{2}\right)g=2y-2tv_{0}-2h$$

Divide both sides by -t^{2}.

$$\frac{\left(-t^{2}\right)g}{-t^{2}}=\frac{2y-2tv_{0}-2h}{-t^{2}}$$

Dividing by -t^{2} undoes the multiplication by -t^{2}.

$$g=\frac{2y-2tv_{0}-2h}{-t^{2}}$$

Divide 2y-2tv_{0}-2h by -t^{2}.

$$g=-\frac{2\left(y-tv_{0}-h\right)}{t^{2}}$$

Solve for g

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

Steps for Solving Linear Equation

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

$$h+v_{0}t-\frac{gt^{2}}{2}=y$$

Subtract h from both sides.

$$v_{0}t-\frac{gt^{2}}{2}=y-h$$

Subtract v_{0}t from both sides.

$$-\frac{gt^{2}}{2}=y-h-v_{0}t$$

Multiply both sides of the equation by 2.

$$-gt^{2}=2y-2h-2v_{0}t$$

Reorder the terms.

$$-gt^{2}=2y-2tv_{0}-2h$$

The equation is in standard form.

$$\left(-t^{2}\right)g=2y-2tv_{0}-2h$$

Divide both sides by -t^{2}.

$$\frac{\left(-t^{2}\right)g}{-t^{2}}=\frac{2y-2tv_{0}-2h}{-t^{2}}$$

Dividing by -t^{2} undoes the multiplication by -t^{2}.

$$g=\frac{2y-2tv_{0}-2h}{-t^{2}}$$

Divide 2y-2tv_{0}-2h by -t^{2}.

$$g=-\frac{2\left(y-tv_{0}-h\right)}{t^{2}}$$

Solve for h

$$h=\frac{gt^{2}}{2}-tv_{0}+y$$