Solve for y x=2( cube root of 12+y)

$x = 2 (\sqrt[3]{12 + y})$

Step 1

Rewrite the equation as $2 \sqrt[3]{12 + y} = x$ .

$2 \sqrt[3]{12 + y} = x$

Step 2

Divide each term in $2 \sqrt[3]{12 + y} = x$ by $2$ and simplify.

Divide each term in $2 \sqrt[3]{12 + y} = x$ by $2$ .

$\frac{2 \sqrt[3]{12 + y}}{2} = \frac{x}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 \sqrt[3]{12 + y}}{2} = \frac{x}{2}$

Divide $\sqrt[3]{12 + y}$ by $1$ .

$\sqrt[3]{12 + y} = \frac{x}{2}$

Step 3

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

${\sqrt[3]{12 + y}}^{3} = {(\frac{x}{2})}^{3}$

Step 4

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{12 + y}$ as ${(12 + y)}^{\frac{1}{3}}$ .

${({(12 + y)}^{\frac{1}{3}})}^{3} = {(\frac{x}{2})}^{3}$

Simplify the left side.

Simplify ${({(12 + y)}^{\frac{1}{3}})}^{3}$ .

Multiply the exponents in ${({(12 + y)}^{\frac{1}{3}})}^{3}$ .

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

${(12 + y)}^{\frac{1}{3} \cdot 3} = {(\frac{x}{2})}^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

${(12 + y)}^{\frac{1}{3} \cdot 3} = {(\frac{x}{2})}^{3}$

Rewrite the expression.

${(12 + y)}^{1} = {(\frac{x}{2})}^{3}$

Simplify.

$12 + y = {(\frac{x}{2})}^{3}$

Simplify the right side.

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

Apply the product rule to $\frac{x}{2}$ .

$12 + y = \frac{x^{3}}{2^{3}}$

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

$12 + y = \frac{x^{3}}{8}$

Step 5

Subtract $12$ from both sides of the equation.

$y = \frac{x^{3}}{8} - 12$