Precalculus Examples

$H (t) = 36 t - 6 t^{2}$

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.

$36 t - 6 t^{2} = H t$

Step 2

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

$36 t - 6 t^{2} - H t = 0$

Step 3

Factor $t$ out of $36 t - 6 t^{2} - H t$ .

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Step 3.1

Factor $t$ out of $36 t$ .

$t \cdot 36 - 6 t^{2} - H t = 0$

Step 3.2

Factor $t$ out of $- 6 t^{2}$ .

$t \cdot 36 + t (- 6 t) - H t = 0$

Step 3.3

Factor $t$ out of $- H t$ .

$t \cdot 36 + t (- 6 t) + t (- H) = 0$

Step 3.4

Factor $t$ out of $t \cdot 36 + t (- 6 t)$ .

$t \cdot (36 - 6 t) + t (- H) = 0$

Step 3.5

Factor $t$ out of $t \cdot (36 - 6 t) + t (- H)$ .

$t (36 - 6 t - H) = 0$

Step 4

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

$t = 0$

$36 - 6 t - H = 0$

Step 5

Set $t$ equal to $0$ .

$t = 0$

Step 6

Set $36 - 6 t - H$ equal to $0$ and solve for $t$ .

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Step 6.1

Set $36 - 6 t - H$ equal to $0$ .

$36 - 6 t - H = 0$

Step 6.2

Solve $36 - 6 t - H = 0$ for $t$ .

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Step 6.2.1

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

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Step 6.2.1.1

Subtract $36$ from both sides of the equation.

$- 6 t - H = - 36$

Step 6.2.1.2

Add $H$ to both sides of the equation.

$- 6 t = - 36 + H$

Step 6.2.2

Divide each term in $- 6 t = - 36 + H$ by $- 6$ and simplify.

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Step 6.2.2.1

Divide each term in $- 6 t = - 36 + H$ by $- 6$ .

$\frac{- 6 t}{- 6} = \frac{- 36}{- 6} + \frac{H}{- 6}$

Step 6.2.2.2

Simplify the left side.

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Step 6.2.2.2.1

Cancel the common factor of $- 6$ .

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Step 6.2.2.2.1.1

Cancel the common factor.

$\frac{- 6 t}{- 6} = \frac{- 36}{- 6} + \frac{H}{- 6}$

Step 6.2.2.2.1.2

Divide $t$ by $1$ .

$t = \frac{- 36}{- 6} + \frac{H}{- 6}$

Step 6.2.2.3

Simplify the right side.

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Step 6.2.2.3.1

Simplify each term.

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Step 6.2.2.3.1.1

Divide $- 36$ by $- 6$ .

$t = 6 + \frac{H}{- 6}$

Step 6.2.2.3.1.2

Move the negative in front of the fraction.

$t = 6 - \frac{H}{6}$

Step 7

The final solution is all the values that make $t (36 - 6 t - H) = 0$ true.

$t = 0$

$t = 6 - \frac{H}{6}$