Solve s=ut-1/2gt^2

$$s = u t - \frac { 1 } { 2 } g t ^ { 2 }$$

Solve for g

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

Steps for Solving Linear Equation

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

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

Subtract ut from both sides.

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

The equation is in standard form.

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

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

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

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

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

Divide s-tu by -\frac{1}{2}t^{2}.

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

Solve for s

$$s=-\frac{t\left(gt-2u\right)}{2}$$