Solve for x cube root of 2x+6=-8

$\sqrt[3]{2 x} + 6 = - 8$

Move all terms not containing $\sqrt[3]{2 x}$ to the right side of the equation.

Subtract $6$ from both sides of the equation.

$\sqrt[3]{2 x} = - 8 - 6$

Subtract $6$ from $- 8$ .

$\sqrt[3]{2 x} = - 14$

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

${\sqrt[3]{2 x}}^{3} = {(- 14)}^{3}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{2 x}$ as ${(2 x)}^{\frac{1}{3}}$ .

${({(2 x)}^{\frac{1}{3}})}^{3} = {(- 14)}^{3}$

Simplify the left side.

Simplify ${({(2 x)}^{\frac{1}{3}})}^{3}$ .

Multiply the exponents in ${({(2 x)}^{\frac{1}{3}})}^{3}$ .

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

${(2 x)}^{\frac{1}{3} \cdot 3} = {(- 14)}^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

${(2 x)}^{\frac{1}{3} \cdot 3} = {(- 14)}^{3}$

Rewrite the expression.

${(2 x)}^{1} = {(- 14)}^{3}$

Simplify.

$2 x = {(- 14)}^{3}$

Simplify the right side.

Raise $- 14$ to the power of $3$ .

$2 x = - 2744$

Divide each term in $2 x = - 2744$ by $2$ and simplify.

Divide each term in $2 x = - 2744$ by $2$ .

$\frac{2 x}{2} = \frac{- 2744}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 2744}{2}$

Divide $x$ by $1$ .

$x = \frac{- 2744}{2}$

Simplify the right side.

Divide $- 2744$ by $2$ .

$x = - 1372$