Solve for a h=-15t+1/2at^2+9

$h = - 15 t + \frac{1}{2} a t^{2} + 9$

Rewrite the equation as $- 15 t + \frac{1}{2} \cdot (a t^{2}) + 9 = h$ .

$- 15 t + \frac{1}{2} \cdot (a t^{2}) + 9 = h$

Multiply $\frac{1}{2} (a t^{2})$ .

Combine $a$ and $\frac{1}{2}$ .

$- 15 t + \frac{a}{2} t^{2} + 9 = h$

Combine $\frac{a}{2}$ and $t^{2}$ .

$- 15 t + \frac{a t^{2}}{2} + 9 = h$

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

Add $15 t$ to both sides of the equation.

$\frac{a t^{2}}{2} + 9 = h + 15 t$

Subtract $9$ from both sides of the equation.

$\frac{a t^{2}}{2} = h + 15 t - 9$

Multiply both sides of the equation by $2$ .

$2 \frac{a t^{2}}{2} = 2 (h + 15 t - 9)$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$2 \frac{a t^{2}}{2} = 2 (h + 15 t - 9)$

Rewrite the expression.

$a t^{2} = 2 (h + 15 t - 9)$

Simplify the right side.

Simplify $2 (h + 15 t - 9)$ .

Apply the distributive property.

$a t^{2} = 2 h + 2 (15 t) + 2 \cdot - 9$

Simplify.

Multiply $15$ by $2$ .

$a t^{2} = 2 h + 30 t + 2 \cdot - 9$

Multiply $2$ by $- 9$ .

$a t^{2} = 2 h + 30 t - 18$

Divide each term in $a t^{2} = 2 h + 30 t - 18$ by $t^{2}$ and simplify.

Divide each term in $a t^{2} = 2 h + 30 t - 18$ by $t^{2}$ .

$\frac{a t^{2}}{t^{2}} = \frac{2 h}{t^{2}} + \frac{30 t}{t^{2}} + \frac{- 18}{t^{2}}$

Simplify the left side.

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

Cancel the common factor.

$\frac{a t^{2}}{t^{2}} = \frac{2 h}{t^{2}} + \frac{30 t}{t^{2}} + \frac{- 18}{t^{2}}$

Divide $a$ by $1$ .

$a = \frac{2 h}{t^{2}} + \frac{30 t}{t^{2}} + \frac{- 18}{t^{2}}$

Simplify the right side.

Simplify each term.

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

Factor $t$ out of $30 t$ .

$a = \frac{2 h}{t^{2}} + \frac{t \cdot 30}{t^{2}} + \frac{- 18}{t^{2}}$

Cancel the common factors.

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

$a = \frac{2 h}{t^{2}} + \frac{t \cdot 30}{t \cdot t} + \frac{- 18}{t^{2}}$

Cancel the common factor.

$a = \frac{2 h}{t^{2}} + \frac{t \cdot 30}{t \cdot t} + \frac{- 18}{t^{2}}$

Rewrite the expression.

$a = \frac{2 h}{t^{2}} + \frac{30}{t} + \frac{- 18}{t^{2}}$

Move the negative in front of the fraction.

$a = \frac{2 h}{t^{2}} + \frac{30}{t} - \frac{18}{t^{2}}$

Solve for a h=-15t+1/2at^2+9

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