Solve for g
\left\{\begin{matrix}g=\frac{2E-mv^{2}}{2hm}\text{, }&h\neq 0\text{ and }m\neq 0\\g\in \mathrm{R}\text{, }&\left(E=\frac{mv^{2}}{2}\text{ and }h=0\right)\text{ or }\left(E=0\text{ and }m=0\text{ and }h\neq 0\right)\end{matrix}\right.
Solve for E
E=\frac{m\left(v^{2}+2gh\right)}{2}
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\frac{1}{2}mv^{2}+mgh=E
Swap sides so that all variable terms are on the left hand side.
mgh=E-\frac{1}{2}mv^{2}
Subtract \frac{1}{2}mv^{2} from both sides.
hmg=-\frac{mv^{2}}{2}+E
The equation is in standard form.
\frac{hmg}{hm}=\frac{-\frac{mv^{2}}{2}+E}{hm}
Divide both sides by mh.
g=\frac{-\frac{mv^{2}}{2}+E}{hm}
Dividing by mh undoes the multiplication by mh.
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