Solve s=1/2gt^2+v_{0}tquadd

$$s = \frac { 1 } { 2 } g t ^ { 2 } + v _ { 0 } t \quad d$$

Solve for d

$$\left\{\begin{matrix}d=\frac{2s-gt^{2}}{2tv_{0}}\text{, }&t\neq 0\text{ and }v_{0}\neq 0\\d\in \mathrm{R}\text{, }&\left(s=0\text{ and }t=0\right)\text{ or }\left(s=\frac{gt^{2}}{2}\text{ and }v_{0}=0\text{ and }t\neq 0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$\frac{1}{2}gt^{2}+v_{0}td=s$$

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

$$v_{0}td=s-\frac{1}{2}gt^{2}$$

The equation is in standard form.

$$tv_{0}d=-\frac{gt^{2}}{2}+s$$

Divide both sides by v_{0}t.

$$\frac{tv_{0}d}{tv_{0}}=\frac{-\frac{gt^{2}}{2}+s}{tv_{0}}$$

Dividing by v_{0}t undoes the multiplication by v_{0}t.

$$d=\frac{-\frac{gt^{2}}{2}+s}{tv_{0}}$$

Solve for g

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

Steps for Solving Linear Equation

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

$$\frac{1}{2}gt^{2}+v_{0}td=s$$

Subtract v_{0}td from both sides.

$$\frac{1}{2}gt^{2}=s-v_{0}td$$

Reorder the terms.

$$\frac{1}{2}gt^{2}=s-dtv_{0}$$

The equation is in standard form.

$$\frac{t^{2}}{2}g=s-dtv_{0}$$

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

$$\frac{2\times \frac{t^{2}}{2}g}{t^{2}}=\frac{2\left(s-dtv_{0}\right)}{t^{2}}$$

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

$$g=\frac{2\left(s-dtv_{0}\right)}{t^{2}}$$