Calculus Examples

$0 = \frac{y (12 - y)}{{(y^{2} - 2 y + 12)}^{2}}$

Step 1

Set the numerator equal to zero.

$y (12 - y) = 0$

Step 2

Solve the equation for $y$ .

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Step 2.1

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

$y = 0$

$12 - y = 0$

Step 2.2

Set $y$ equal to $0$ .

$y = 0$

Step 2.3

Set $12 - y$ equal to $0$ and solve for $y$ .

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Step 2.3.1

Set $12 - y$ equal to $0$ .

$12 - y = 0$

Step 2.3.2

Solve $12 - y = 0$ for $y$ .

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Step 2.3.2.1

Subtract $12$ from both sides of the equation.

$- y = - 12$

Step 2.3.2.2

Divide each term in $- y = - 12$ by $- 1$ and simplify.

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Step 2.3.2.2.1

Divide each term in $- y = - 12$ by $- 1$ .

$\frac{- y}{- 1} = \frac{- 12}{- 1}$

Step 2.3.2.2.2

Simplify the left side.

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Step 2.3.2.2.2.1

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{- 12}{- 1}$

Step 2.3.2.2.2.2

Divide $y$ by $1$ .

$y = \frac{- 12}{- 1}$

Step 2.3.2.2.3

Simplify the right side.

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Step 2.3.2.2.3.1

Divide $- 12$ by $- 1$ .

$y = 12$

Step 2.4

The final solution is all the values that make $y (12 - y) = 0$ true.

$y = 0, 12$