Solve for h (V_f)^2=(V_o)^2+2gh

${(V_{f})}^{2} = {(V_{o})}^{2} + 2 g h$

Rewrite the equation as ${V_{o}}^{2} + 2 g h = {V_{f}}^{2}$ .

${V_{o}}^{2} + 2 g h = {V_{f}}^{2}$

Subtract ${V_{o}}^{2}$ from both sides of the equation.

$2 g h = {V_{f}}^{2} - {V_{o}}^{2}$

Divide each term in $2 g h = {V_{f}}^{2} - {V_{o}}^{2}$ by $2 g$ and simplify.

Divide each term in $2 g h = {V_{f}}^{2} - {V_{o}}^{2}$ by $2 g$ .

$\frac{2 g h}{2 g} = \frac{{V_{f}}^{2}}{2 g} + \frac{- {V_{o}}^{2}}{2 g}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 g h}{2 g} = \frac{{V_{f}}^{2}}{2 g} + \frac{- {V_{o}}^{2}}{2 g}$

Rewrite the expression.

$\frac{g h}{g} = \frac{{V_{f}}^{2}}{2 g} + \frac{- {V_{o}}^{2}}{2 g}$

Cancel the common factor of $g$ .

Cancel the common factor.

$\frac{g h}{g} = \frac{{V_{f}}^{2}}{2 g} + \frac{- {V_{o}}^{2}}{2 g}$

Divide $h$ by $1$ .

$h = \frac{{V_{f}}^{2}}{2 g} + \frac{- {V_{o}}^{2}}{2 g}$

Simplify the right side.

Move the negative in front of the fraction.

$h = \frac{{V_{f}}^{2}}{2 g} - \frac{{V_{o}}^{2}}{2 g}$