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Solve for g
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u^{2}+2gh=v^{2}
Swap sides so that all variable terms are on the left hand side.
2gh=v^{2}-u^{2}
Subtract u^{2} from both sides.
2hg=v^{2}-u^{2}
The equation is in standard form.
\frac{2hg}{2h}=\frac{\left(v-u\right)\left(u+v\right)}{2h}
Divide both sides by 2h.
g=\frac{\left(v-u\right)\left(u+v\right)}{2h}
Dividing by 2h undoes the multiplication by 2h.
u^{2}+2gh=v^{2}
Swap sides so that all variable terms are on the left hand side.
2gh=v^{2}-u^{2}
Subtract u^{2} from both sides.
\frac{2gh}{2g}=\frac{\left(v-u\right)\left(u+v\right)}{2g}
Divide both sides by 2g.
h=\frac{\left(v-u\right)\left(u+v\right)}{2g}
Dividing by 2g undoes the multiplication by 2g.