Solve for v h=-16t^2+vt+k

$h = - 16 t^{2} + v t + k$

Step 1

Rewrite the equation as $- 16 t^{2} + v t + k = h$ .

$- 16 t^{2} + v t + k = h$

Step 2

Move all terms not containing $v$ to the right side of the equation.

Add $16 t^{2}$ to both sides of the equation.

$v t + k = h + 16 t^{2}$

Subtract $k$ from both sides of the equation.

$v t = h + 16 t^{2} - k$

Step 3

Divide each term in $v t = h + 16 t^{2} - k$ by $t$ and simplify.

Divide each term in $v t = h + 16 t^{2} - k$ by $t$ .

$\frac{v t}{t} = \frac{h}{t} + \frac{16 t^{2}}{t} + \frac{- k}{t}$

Simplify the left side.

Cancel the common factor of $t$ .

Cancel the common factor.

$\frac{v t}{t} = \frac{h}{t} + \frac{16 t^{2}}{t} + \frac{- k}{t}$

Divide $v$ by $1$ .

$v = \frac{h}{t} + \frac{16 t^{2}}{t} + \frac{- k}{t}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $t^{2}$ and $t$ .

Factor $t$ out of $16 t^{2}$ .

$v = \frac{h}{t} + \frac{t (16 t)}{t} + \frac{- k}{t}$

Cancel the common factors.

Raise $t$ to the power of $1$ .

$v = \frac{h}{t} + \frac{t (16 t)}{t^{1}} + \frac{- k}{t}$

Factor $t$ out of $t^{1}$ .

$v = \frac{h}{t} + \frac{t (16 t)}{t \cdot 1} + \frac{- k}{t}$

Cancel the common factor.

$v = \frac{h}{t} + \frac{t (16 t)}{t \cdot 1} + \frac{- k}{t}$

Rewrite the expression.

$v = \frac{h}{t} + \frac{16 t}{1} + \frac{- k}{t}$

Divide $16 t$ by $1$ .

$v = \frac{h}{t} + 16 t + \frac{- k}{t}$

Move the negative in front of the fraction.

$v = \frac{h}{t} + 16 t - \frac{k}{t}$