Solve for x cube root of x+4+ cube root of 2x+8=0

$\sqrt[3]{x + 4} + \sqrt[3]{2 x + 8} = 0$

Solve for $\sqrt[3]{x + 4}$ .

Factor $2$ out of $2 x + 8$ .

Factor $2$ out of $2 x$ .

$\sqrt[3]{x + 4} + \sqrt[3]{2 (x) + 8} = 0$

Factor $2$ out of $8$ .

$\sqrt[3]{x + 4} + \sqrt[3]{2 x + 2 \cdot 4} = 0$

Factor $2$ out of $2 x + 2 \cdot 4$ .

$\sqrt[3]{x + 4} + \sqrt[3]{2 (x + 4)} = 0$

Subtract $\sqrt[3]{2 (x + 4)}$ from both sides of the equation.

$\sqrt[3]{x + 4} = - \sqrt[3]{2 (x + 4)}$

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

${\sqrt[3]{x + 4}}^{3} = {(- \sqrt[3]{2 (x + 4)})}^{3}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{x + 4}$ as ${(x + 4)}^{\frac{1}{3}}$ .

${({(x + 4)}^{\frac{1}{3}})}^{3} = {(- \sqrt[3]{2 (x + 4)})}^{3}$

Simplify the left side.

Simplify ${({(x + 4)}^{\frac{1}{3}})}^{3}$ .

Multiply the exponents in ${({(x + 4)}^{\frac{1}{3}})}^{3}$ .

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

${(x + 4)}^{\frac{1}{3} \cdot 3} = {(- \sqrt[3]{2 (x + 4)})}^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

${(x + 4)}^{\frac{1}{3} \cdot 3} = {(- \sqrt[3]{2 (x + 4)})}^{3}$

Rewrite the expression.

${(x + 4)}^{1} = {(- \sqrt[3]{2 (x + 4)})}^{3}$

Simplify.

$x + 4 = {(- \sqrt[3]{2 (x + 4)})}^{3}$

Simplify the right side.

Simplify ${(- \sqrt[3]{2 (x + 4)})}^{3}$ .

Simplify the expression.

Apply the product rule to $- \sqrt[3]{2 (x + 4)}$ .

$x + 4 = {(- 1)}^{3} {\sqrt[3]{2 (x + 4)}}^{3}$

Raise $- 1$ to the power of $3$ .

$x + 4 = - {\sqrt[3]{2 (x + 4)}}^{3}$

Rewrite ${\sqrt[3]{2 (x + 4)}}^{3}$ as $2 (x + 4)$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{2 (x + 4)}$ as ${(2 (x + 4))}^{\frac{1}{3}}$ .

$x + 4 = - {({(2 (x + 4))}^{\frac{1}{3}})}^{3}$

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

$x + 4 = - {(2 (x + 4))}^{\frac{1}{3} \cdot 3}$

Combine $\frac{1}{3}$ and $3$ .

$x + 4 = - {(2 (x + 4))}^{\frac{3}{3}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$x + 4 = - {(2 (x + 4))}^{\frac{3}{3}}$

Rewrite the expression.

$x + 4 = - {(2 (x + 4))}^{1}$

Simplify.

$x + 4 = - (2 (x + 4))$

Apply the distributive property.

$x + 4 = - (2 x + 2 \cdot 4)$

Multiply $2$ by $4$ .

$x + 4 = - (2 x + 8)$

Apply the distributive property.

$x + 4 = - (2 x) - 1 \cdot 8$

Multiply.

Multiply $2$ by $- 1$ .

$x + 4 = - 2 x - 1 \cdot 8$

Multiply $- 1$ by $8$ .

$x + 4 = - 2 x - 8$

Solve for $x$ .

Move all terms containing $x$ to the left side of the equation.

Add $2 x$ to both sides of the equation.

$x + 4 + 2 x = - 8$

Add $x$ and $2 x$ .

$3 x + 4 = - 8$

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

Subtract $4$ from both sides of the equation.

$3 x = - 8 - 4$

Subtract $4$ from $- 8$ .

$3 x = - 12$

Divide each term in $3 x = - 12$ by $3$ and simplify.

Divide each term in $3 x = - 12$ by $3$ .

$\frac{3 x}{3} = \frac{- 12}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 12}{3}$

Divide $x$ by $1$ .

$x = \frac{- 12}{3}$

Simplify the right side.

Divide $- 12$ by $3$ .

$x = - 4$

Solve for x cube root of x+4+ cube root of 2x+8=0

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