Solve for t h(t)=-16t^2+64t

$h (t) = - 16 t^{2} + 64 t$

Step 1

Since $t$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$- 16 t^{2} + 64 t = h t$

Step 2

Subtract $h t$ from both sides of the equation.

$- 16 t^{2} + 64 t - h t = 0$

Step 3

Factor $t$ out of $- 16 t^{2} + 64 t - h t$ .

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

$t (- 16 t) + 64 t - h t = 0$

Factor $t$ out of $64 t$ .

$t (- 16 t) + t \cdot 64 - h t = 0$

Factor $t$ out of $- h t$ .

$t (- 16 t) + t \cdot 64 + t (- h) = 0$

Factor $t$ out of $t (- 16 t) + t \cdot 64$ .

$t (- 16 t + 64) + t (- h) = 0$

Factor $t$ out of $t (- 16 t + 64) + t (- h)$ .

$t (- 16 t + 64 - h) = 0$

Step 4

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$t = 0$

$- 16 t + 64 - h = 0$

Step 5

Set $t$ equal to $0$ .

$t = 0$

Step 6

Set $- 16 t + 64 - h$ equal to $0$ and solve for $t$ .

Set $- 16 t + 64 - h$ equal to $0$ .

$- 16 t + 64 - h = 0$

Solve $- 16 t + 64 - h = 0$ for $t$ .

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

Subtract $64$ from both sides of the equation.

$- 16 t - h = - 64$

Add $h$ to both sides of the equation.

$- 16 t = - 64 + h$

Divide each term in $- 16 t = - 64 + h$ by $- 16$ and simplify.

Divide each term in $- 16 t = - 64 + h$ by $- 16$ .

$\frac{- 16 t}{- 16} = \frac{- 64}{- 16} + \frac{h}{- 16}$

Simplify the left side.

Cancel the common factor of $- 16$ .

Cancel the common factor.

$\frac{- 16 t}{- 16} = \frac{- 64}{- 16} + \frac{h}{- 16}$

Divide $t$ by $1$ .

$t = \frac{- 64}{- 16} + \frac{h}{- 16}$

Simplify the right side.

Simplify each term.

Divide $- 64$ by $- 16$ .

$t = 4 + \frac{h}{- 16}$

Move the negative in front of the fraction.

$t = 4 - \frac{h}{16}$

Step 7

The final solution is all the values that make $t (- 16 t + 64 - h) = 0$ true.

$t = 0$

$t = 4 - \frac{h}{16}$

Solve for t h(t)=-16t^2+64t

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