Solve for y x=3( cube root of 15+y)

$x = 3 (\sqrt[3]{15 + y})$

Rewrite the equation as $3 \sqrt[3]{15 + y} = x$ .

$3 \sqrt[3]{15 + y} = x$

Divide each term in $3 \sqrt[3]{15 + y} = x$ by $3$ and simplify.

Divide each term in $3 \sqrt[3]{15 + y} = x$ by $3$ .

$\frac{3 \sqrt[3]{15 + y}}{3} = \frac{x}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 \sqrt[3]{15 + y}}{3} = \frac{x}{3}$

Divide $\sqrt[3]{15 + y}$ by $1$ .

$\sqrt[3]{15 + y} = \frac{x}{3}$

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

${\sqrt[3]{15 + y}}^{3} = {(\frac{x}{3})}^{3}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{15 + y}$ as ${(15 + y)}^{\frac{1}{3}}$ .

${({(15 + y)}^{\frac{1}{3}})}^{3} = {(\frac{x}{3})}^{3}$

Simplify the left side.

Simplify ${({(15 + y)}^{\frac{1}{3}})}^{3}$ .

Multiply the exponents in ${({(15 + y)}^{\frac{1}{3}})}^{3}$ .

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

${(15 + y)}^{\frac{1}{3} \cdot 3} = {(\frac{x}{3})}^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

${(15 + y)}^{\frac{1}{3} \cdot 3} = {(\frac{x}{3})}^{3}$

Rewrite the expression.

${(15 + y)}^{1} = {(\frac{x}{3})}^{3}$

Simplify.

$15 + y = {(\frac{x}{3})}^{3}$

Simplify the right side.

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

Apply the product rule to $\frac{x}{3}$ .

$15 + y = \frac{x^{3}}{3^{3}}$

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

$15 + y = \frac{x^{3}}{27}$

Subtract $15$ from both sides of the equation.

$y = \frac{x^{3}}{27} - 15$