Solve for x y=5(x^3+4)

$y = 5 (x^{3} + 4)$

Rewrite the equation as $5 (x^{3} + 4) = y$ .

$5 (x^{3} + 4) = y$

Divide each term in $5 (x^{3} + 4) = y$ by $5$ and simplify.

Divide each term in $5 (x^{3} + 4) = y$ by $5$ .

$\frac{5 (x^{3} + 4)}{5} = \frac{y}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 (x^{3} + 4)}{5} = \frac{y}{5}$

Divide $x^{3} + 4$ by $1$ .

$x^{3} + 4 = \frac{y}{5}$

Subtract $4$ from both sides of the equation.

$x^{3} = \frac{y}{5} - 4$

Take the cube root of both sides of the equation to eliminate the exponent on the left side.

$x = \sqrt[3]{\frac{y}{5} - 4}$

Simplify $\sqrt[3]{\frac{y}{5} - 4}$ .

To write $- 4$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$x = \sqrt[3]{\frac{y}{5} - 4 \cdot \frac{5}{5}}$

Combine $- 4$ and $\frac{5}{5}$ .

$x = \sqrt[3]{\frac{y}{5} + \frac{- 4 \cdot 5}{5}}$

Combine the numerators over the common denominator.

$x = \sqrt[3]{\frac{y - 4 \cdot 5}{5}}$

Multiply $- 4$ by $5$ .

$x = \sqrt[3]{\frac{y - 20}{5}}$

Rewrite $\sqrt[3]{\frac{y - 20}{5}}$ as $\frac{\sqrt[3]{y - 20}}{\sqrt[3]{5}}$ .

$x = \frac{\sqrt[3]{y - 20}}{\sqrt[3]{5}}$

Multiply $\frac{\sqrt[3]{y - 20}}{\sqrt[3]{5}}$ by $\frac{{\sqrt[3]{5}}^{2}}{{\sqrt[3]{5}}^{2}}$ .

$x = \frac{\sqrt[3]{y - 20}}{\sqrt[3]{5}} \cdot \frac{{\sqrt[3]{5}}^{2}}{{\sqrt[3]{5}}^{2}}$

Combine and simplify the denominator.

Multiply $\frac{\sqrt[3]{y - 20}}{\sqrt[3]{5}}$ by $\frac{{\sqrt[3]{5}}^{2}}{{\sqrt[3]{5}}^{2}}$ .

$x = \frac{\sqrt[3]{y - 20} {\sqrt[3]{5}}^{2}}{\sqrt[3]{5} {\sqrt[3]{5}}^{2}}$

Raise $\sqrt[3]{5}$ to the power of $1$ .

$x = \frac{\sqrt[3]{y - 20} {\sqrt[3]{5}}^{2}}{{\sqrt[3]{5}}^{1} {\sqrt[3]{5}}^{2}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x = \frac{\sqrt[3]{y - 20} {\sqrt[3]{5}}^{2}}{{\sqrt[3]{5}}^{1 + 2}}$

Add $1$ and $2$ .

$x = \frac{\sqrt[3]{y - 20} {\sqrt[3]{5}}^{2}}{{\sqrt[3]{5}}^{3}}$

Rewrite ${\sqrt[3]{5}}^{3}$ as $5$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{5}$ as $5^{\frac{1}{3}}$ .

$x = \frac{\sqrt[3]{y - 20} {\sqrt[3]{5}}^{2}}{{(5^{\frac{1}{3}})}^{3}}$

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

$x = \frac{\sqrt[3]{y - 20} {\sqrt[3]{5}}^{2}}{5^{\frac{1}{3} \cdot 3}}$

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

$x = \frac{\sqrt[3]{y - 20} {\sqrt[3]{5}}^{2}}{5^{\frac{3}{3}}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$x = \frac{\sqrt[3]{y - 20} {\sqrt[3]{5}}^{2}}{5^{\frac{3}{3}}}$

Rewrite the expression.

$x = \frac{\sqrt[3]{y - 20} {\sqrt[3]{5}}^{2}}{5^{1}}$

Evaluate the exponent.

$x = \frac{\sqrt[3]{y - 20} {\sqrt[3]{5}}^{2}}{5}$

Simplify the numerator.

Rewrite ${\sqrt[3]{5}}^{2}$ as ${(5^{2})}^{\frac{1}{3}}$ .

$x = \frac{\sqrt[3]{y - 20} \sqrt[3]{5^{2}}}{5}$

Raise $5$ to the power of $2$ .

$x = \frac{\sqrt[3]{y - 20} \sqrt[3]{25}}{5}$

Simplify with factoring out.

Combine using the product rule for radicals.

$x = \frac{\sqrt[3]{(y - 20) \cdot 25}}{5}$

Reorder factors in $\frac{\sqrt[3]{(y - 20) \cdot 25}}{5}$ .

$x = \frac{\sqrt[3]{25 (y - 20)}}{5}$

Solve for x y=5(x^3+4)

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