Calculus Examples

$144 p r - 6 p^{2} r^{2} = 0$

Step 1

Factor $6 p r$ out of $144 p r - 6 p^{2} r^{2}$ .

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Step 1.1

Factor $6 p r$ out of $144 p r$ .

$6 p r (24) - 6 p^{2} r^{2} = 0$

Step 1.2

Factor $6 p r$ out of $- 6 p^{2} r^{2}$ .

$6 p r (24) + 6 p r (- p r) = 0$

Step 1.3

Factor $6 p r$ out of $6 p r (24) + 6 p r (- p r)$ .

$6 p r (24 - p r) = 0$

Step 2

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

$r = 0$

$24 - p r = 0$

Step 3

Set $r$ equal to $0$ .

$r = 0$

Step 4

Set $24 - p r$ equal to $0$ and solve for $r$ .

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Step 4.1

Set $24 - p r$ equal to $0$ .

$24 - p r = 0$

Step 4.2

Solve $24 - p r = 0$ for $r$ .

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Step 4.2.1

Subtract $24$ from both sides of the equation.

$- p r = - 24$

Step 4.2.2

Divide each term in $- p r = - 24$ by $- p$ and simplify.

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Step 4.2.2.1

Divide each term in $- p r = - 24$ by $- p$ .

$\frac{- p r}{- p} = \frac{- 24}{- p}$

Step 4.2.2.2

Simplify the left side.

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Step 4.2.2.2.1

Dividing two negative values results in a positive value.

$\frac{p r}{p} = \frac{- 24}{- p}$

Step 4.2.2.2.2

Cancel the common factor of $p$ .

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Step 4.2.2.2.2.1

Cancel the common factor.

$\frac{p r}{p} = \frac{- 24}{- p}$

Step 4.2.2.2.2.2

Divide $r$ by $1$ .

$r = \frac{- 24}{- p}$

Step 4.2.2.3

Simplify the right side.

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Step 4.2.2.3.1

Dividing two negative values results in a positive value.

$r = \frac{24}{p}$

Step 5

The final solution is all the values that make $6 p r (24 - p r) = 0$ true.

$r = 0$

$r = \frac{24}{p}$