Solve by Factoring cube root of 6x=-3

$\sqrt[3]{6 x} = - 3$

Move $3$ to the left side of the equation by adding it to both sides.

$\sqrt[3]{6 x} + 3 = 0$

Subtract $3$ from both sides of the equation.

$\sqrt[3]{6 x} = - 3$

To remove the radical on the left side of the equation, cube both sides of the equation.

${\sqrt[3]{6 x}}^{3} = {(- 3)}^{3}$

Simplify each side of the equation.

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Multiply the exponents in ${({(6 x)}^{\frac{1}{3}})}^{3}$ .

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Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(6 x)}^{\frac{1}{3} \cdot 3} = {(- 3)}^{3}$

Cancel the common factor of $3$ .

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Cancel the common factor.

${(6 x)}^{\frac{1}{3} \cdot 3} = {(- 3)}^{3}$

Rewrite the expression.

${(6 x)}^{1} = {(- 3)}^{3}$

Simplify.

$6 x = {(- 3)}^{3}$

Raise $- 3$ to the power of $3$ .

$6 x = - 27$

Divide each term by $6$ and simplify.

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Divide each term in $6 x = - 27$ by $6$ .

$\frac{6 x}{6} = \frac{- 27}{6}$

Cancel the common factor of $6$ .

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Cancel the common factor.

$\frac{6 x}{6} = \frac{- 27}{6}$

Divide $x$ by $1$ .

$x = \frac{- 27}{6}$

Simplify $\frac{- 27}{6}$ .

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Cancel the common factor of $- 27$ and $6$ .

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Factor $3$ out of $- 27$ .

$x = \frac{3 (- 9)}{6}$

Cancel the common factors.

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Factor $3$ out of $6$ .

$x = \frac{3 \cdot - 9}{3 \cdot 2}$

Cancel the common factor.

$x = \frac{3 \cdot - 9}{3 \cdot 2}$

Rewrite the expression.

$x = \frac{- 9}{2}$

Move the negative in front of the fraction.

$x = - \frac{9}{2}$

Solve by Factoring cube root of 6x=-3

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