Solve s_{y}=1/2*g*t^2

$$s _ { y } = \frac { 1 } { 2 } \cdot g \cdot t ^ { 2 }$$

Solve for g

$$\left\{\begin{matrix}g=\frac{2s_{y}}{t^{2}}\text{, }&t\neq 0\\g\in \mathrm{R}\text{, }&s_{y}=0\text{ and }t=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$\frac{1}{2}gt^{2}=s_{y}$$

The equation is in standard form.

$$\frac{t^{2}}{2}g=s_{y}$$

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

$$\frac{2\times \frac{t^{2}}{2}g}{t^{2}}=\frac{2s_{y}}{t^{2}}$$

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

$$g=\frac{2s_{y}}{t^{2}}$$

Solve for s_y

$$s_{y}=\frac{gt^{2}}{2}$$