Algebra Examples

$12$ , $0 = \frac{π}{6} d^{3}$

Step 1

Rewrite the equation as $\frac{π}{6} d^{3} = 0$ .

$\frac{π}{6} d^{3} = 0$

Step 2

Combine $\frac{π}{6}$ and $d^{3}$ .

$\frac{π d^{3}}{6} = 0$

Step 3

Subtract $\frac{π d^{3}}{6}$ from both sides of the equation.

$0 = - \frac{π d^{3}}{6}$

Step 4

Rewrite the equation as $- \frac{π d^{3}}{6} = 0$ .

$- \frac{π d^{3}}{6} = 0$

Step 5

Multiply each term in $- \frac{π d^{3}}{6} = 0$ by $- \frac{6}{π}$ to eliminate the fractions.

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Step 5.1

Multiply each term in $- \frac{π d^{3}}{6} = 0$ by $- \frac{6}{π}$ .

$- \frac{π d^{3}}{6} (- \frac{6}{π}) = 0 (- \frac{6}{π})$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $π$ .

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Step 5.2.1.1

Move the leading negative in $- \frac{π d^{3}}{6}$ into the numerator.

$\frac{- π d^{3}}{6} (- \frac{6}{π}) = 0 (- \frac{6}{π})$

Step 5.2.1.2

Move the leading negative in $- \frac{6}{π}$ into the numerator.

$\frac{- π d^{3}}{6} \cdot \frac{- 6}{π} = 0 (- \frac{6}{π})$

Step 5.2.1.3

Factor $π$ out of $- π d^{3}$ .

$\frac{π (- 1 d^{3})}{6} \cdot \frac{- 6}{π} = 0 (- \frac{6}{π})$

Step 5.2.1.4

Cancel the common factor.

$\frac{π (- 1 d^{3})}{6} \cdot \frac{- 6}{π} = 0 (- \frac{6}{π})$

Step 5.2.1.5

Rewrite the expression.

$\frac{- 1 d^{3}}{6} \cdot - 6 = 0 (- \frac{6}{π})$

Step 5.2.2

Cancel the common factor of $6$ .

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Step 5.2.2.1

Factor $6$ out of $- 6$ .

$\frac{- 1 d^{3}}{6} \cdot (6 (- 1)) = 0 (- \frac{6}{π})$

Step 5.2.2.2

Cancel the common factor.

$\frac{- 1 d^{3}}{6} \cdot (6 \cdot - 1) = 0 (- \frac{6}{π})$

Step 5.2.2.3

Rewrite the expression.

$- 1 d^{3} \cdot - 1 = 0 (- \frac{6}{π})$

Step 5.2.3

Multiply.

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Step 5.2.3.1

Multiply $- 1$ by $- 1$ .

$1 d^{3} = 0 (- \frac{6}{π})$

Step 5.2.3.2

Multiply $d^{3}$ by $1$ .

$d^{3} = 0 (- \frac{6}{π})$

Step 5.3

Simplify the right side.

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Step 5.3.1

Multiply $0 (- \frac{6}{π})$ .

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Step 5.3.1.1

Multiply $- 1$ by $0$ .

$d^{3} = 0 \frac{6}{π}$

Step 5.3.1.2

Multiply $0$ by $\frac{6}{π}$ .

$d^{3} = 0$

Step 6

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$d = \sqrt[3]{0}$

Step 7

Simplify $\sqrt[3]{0}$ .

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Step 7.1

Rewrite $0$ as $0^{3}$ .

$d = \sqrt[3]{0^{3}}$

Step 7.2

Pull terms out from under the radical, assuming real numbers.

$d = 0$

Step 8

Replace the variable $d$ with $0$ in the expression.

$12$