Solve for x (3x+1)^3=64

${(3 x + 1)}^{3} = 64$

Step 1

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

$3 x + 1 = \sqrt[3]{64}$

Step 2

Simplify $\sqrt[3]{64}$ .

Rewrite $64$ as $4^{3}$ .

$3 x + 1 = \sqrt[3]{4^{3}}$

Pull terms out from under the radical, assuming real numbers.

$3 x + 1 = 4$

Step 3

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

Subtract $1$ from both sides of the equation.

$3 x = 4 - 1$

Subtract $1$ from $4$ .

$3 x = 3$

Step 4

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

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

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $3$ by $3$ .

$x = 1$