Solve for x cube root of 6-3x-2=0

$\sqrt[3]{6 - 3 x} - 2 = 0$

Add $2$ to both sides of the equation.

$\sqrt[3]{6 - 3 x} = 2$

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

${\sqrt[3]{6 - 3 x}}^{3} = 2^{3}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{6 - 3 x}$ as ${(6 - 3 x)}^{\frac{1}{3}}$ .

${({(6 - 3 x)}^{\frac{1}{3}})}^{3} = 2^{3}$

Simplify the left side.

Simplify ${({(6 - 3 x)}^{\frac{1}{3}})}^{3}$ .

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

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

${(6 - 3 x)}^{\frac{1}{3} \cdot 3} = 2^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

${(6 - 3 x)}^{\frac{1}{3} \cdot 3} = 2^{3}$

Rewrite the expression.

${(6 - 3 x)}^{1} = 2^{3}$

Simplify.

$6 - 3 x = 2^{3}$

Simplify the right side.

Raise $2$ to the power of $3$ .

$6 - 3 x = 8$

Solve for $x$ .

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

Subtract $6$ from both sides of the equation.

$- 3 x = 8 - 6$

Subtract $6$ from $8$ .

$- 3 x = 2$

Divide each term in $- 3 x = 2$ by $- 3$ and simplify.

Divide each term in $- 3 x = 2$ by $- 3$ .

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

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = - 0.\overline{6}$

Solve for x cube root of 6-3x-2=0

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