Solve for d v_f^2=v_i^2+2ad

${v_{f}}^{2} = {v_{i}}^{2} + 2 a d$

Rewrite the equation as ${v_{i}}^{2} + 2 a d = {v_{f}}^{2}$ .

${v_{i}}^{2} + 2 a d = {v_{f}}^{2}$

Subtract ${v_{i}}^{2}$ from both sides of the equation.

$2 a d = {v_{f}}^{2} - {v_{i}}^{2}$

Divide each term in $2 a d = {v_{f}}^{2} - {v_{i}}^{2}$ by $2 a$ and simplify.

Divide each term in $2 a d = {v_{f}}^{2} - {v_{i}}^{2}$ by $2 a$ .

$\frac{2 a d}{2 a} = \frac{{v_{f}}^{2}}{2 a} + \frac{- {v_{i}}^{2}}{2 a}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 a d}{2 a} = \frac{{v_{f}}^{2}}{2 a} + \frac{- {v_{i}}^{2}}{2 a}$

Rewrite the expression.

$\frac{a d}{a} = \frac{{v_{f}}^{2}}{2 a} + \frac{- {v_{i}}^{2}}{2 a}$

Cancel the common factor of $a$ .

Cancel the common factor.

$\frac{a d}{a} = \frac{{v_{f}}^{2}}{2 a} + \frac{- {v_{i}}^{2}}{2 a}$

Divide $d$ by $1$ .

$d = \frac{{v_{f}}^{2}}{2 a} + \frac{- {v_{i}}^{2}}{2 a}$

Simplify the right side.

Move the negative in front of the fraction.

$d = \frac{{v_{f}}^{2}}{2 a} - \frac{{v_{i}}^{2}}{2 a}$