Solve v^2=u^2+2gs

$$v ^ { 2 } = u ^ { 2 } + 2 g s$$

Solve for g

$$\left\{\begin{matrix}g=-\frac{u^{2}-v^{2}}{2s}\text{, }&s\neq 0\\g\in \mathrm{R}\text{, }&s=0\text{ and }|v|=|u|\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$u^{2}+2gs=v^{2}$$

Subtract u^{2} from both sides.

$$2gs=v^{2}-u^{2}$$

The equation is in standard form.

$$2sg=v^{2}-u^{2}$$

Divide both sides by 2s.

$$\frac{2sg}{2s}=\frac{\left(v-u\right)\left(u+v\right)}{2s}$$

Dividing by 2s undoes the multiplication by 2s.

$$g=\frac{\left(v-u\right)\left(u+v\right)}{2s}$$

Solve for s

$$\left\{\begin{matrix}s=-\frac{u^{2}-v^{2}}{2g}\text{, }&g\neq 0\\s\in \mathrm{R}\text{, }&g=0\text{ and }|v|=|u|\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$u^{2}+2gs=v^{2}$$

Subtract u^{2} from both sides.

$$2gs=v^{2}-u^{2}$$

Divide both sides by 2g.

$$\frac{2gs}{2g}=\frac{\left(v-u\right)\left(u+v\right)}{2g}$$

Dividing by 2g undoes the multiplication by 2g.

$$s=\frac{\left(v-u\right)\left(u+v\right)}{2g}$$