Solve for x 6=10x^3+6

$6 = 10 x^{3} + 6$

Step 1

Rewrite the equation as $10 x^{3} + 6 = 6$ .

$10 x^{3} + 6 = 6$

Step 2

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

Subtract $6$ from both sides of the equation.

$10 x^{3} = 6 - 6$

Subtract $6$ from $6$ .

$10 x^{3} = 0$

Step 3

Divide each term in $10 x^{3} = 0$ by $10$ and simplify.

Divide each term in $10 x^{3} = 0$ by $10$ .

$\frac{10 x^{3}}{10} = \frac{0}{10}$

Simplify the left side.

Cancel the common factor of $10$ .

Cancel the common factor.

$\frac{10 x^{3}}{10} = \frac{0}{10}$

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

$x^{3} = \frac{0}{10}$

Simplify the right side.

Divide $0$ by $10$ .

$x^{3} = 0$

Step 4

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

$x = \sqrt[3]{0}$

Step 5

Simplify $\sqrt[3]{0}$ .

Rewrite $0$ as $0^{3}$ .

$x = \sqrt[3]{0^{3}}$

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

$x = 0$