Solve v^2=u^2+2gh

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

Solve for g

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

Steps for Solving Linear Equation

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

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

Subtract u^{2} from both sides.

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

The equation is in standard form.

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

Divide both sides by 2h.

$$\frac{2hg}{2h}=\frac{\left(v-u\right)\left(u+v\right)}{2h}$$

Dividing by 2h undoes the multiplication by 2h.

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

Solve for h

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

Steps for Solving Linear Equation

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

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

Subtract u^{2} from both sides.

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

Divide both sides by 2g.

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

Dividing by 2g undoes the multiplication by 2g.

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