Set equal to .

Subtract from both sides of the equation.

Move to the left side of the equation by adding it to both sides.

Factor the left side of the equation.

Rewrite as .

Since both terms are perfect cubes, factor using the sum of cubes formula, where and .

Simplify.

Multiply by .

Raise to the power of .

If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .

Set the first factor equal to and solve.

Set the first factor equal to .

Subtract from both sides of the equation.

Set the next factor equal to and solve.

Set the next factor equal to .

Use the quadratic formula to find the solutions.

Substitute the values , , and into the quadratic formula and solve for .

Simplify.

Simplify the numerator.

Raise to the power of .

Multiply by .

Multiply by .

Subtract from .

Rewrite as .

Rewrite as .

Rewrite as .

Rewrite as .

Factor out of .

Rewrite as .

Pull terms out from under the radical.

Move to the left of .

Multiply by .

The final answer is the combination of both solutions.

The final solution is all the values that make true.

Find the Roots (Zeros) f(x)=x^3+27