x^3-2x^2-64x=0

Solution for x^3-2x^2-64x=0 equation:

Simplifying
x3 + -2x2 + -64x = 0

Reorder the terms:
-64x + -2x2 + x3 = 0

Solving
-64x + -2x2 + x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-64 + -2x + x2) = 0

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying
x = 0
Subproblem 2
Set the factor '(-64 + -2x + x2)' equal to zero and attempt to solve:

Simplifying
-64 + -2x + x2 = 0

Solving
-64 + -2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '64' to each side of the equation.
-64 + -2x + 64 + x2 = 0 + 64

Reorder the terms:
-64 + 64 + -2x + x2 = 0 + 64

Combine like terms: -64 + 64 = 0
0 + -2x + x2 = 0 + 64
-2x + x2 = 0 + 64

Combine like terms: 0 + 64 = 64
-2x + x2 = 64

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 64 + 1

Reorder the terms:
1 + -2x + x2 = 64 + 1

Combine like terms: 64 + 1 = 65
1 + -2x + x2 = 65

Factor a perfect square on the left side:
(x + -1)(x + -1) = 65

Calculate the square root of the right side: 8.062257748

Break this problem into two subproblems by setting 
(x + -1) equal to 8.062257748 and -8.062257748.

Subproblem 1
x + -1 = 8.062257748

Simplifying
x + -1 = 8.062257748

Reorder the terms:
-1 + x = 8.062257748

Solving
-1 + x = 8.062257748

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + x = 8.062257748 + 1

Combine like terms: -1 + 1 = 0
0 + x = 8.062257748 + 1
x = 8.062257748 + 1

Combine like terms: 8.062257748 + 1 = 9.062257748
x = 9.062257748

Simplifying
x = 9.062257748

Subproblem 2
x + -1 = -8.062257748

Simplifying
x + -1 = -8.062257748

Reorder the terms:
-1 + x = -8.062257748

Solving
-1 + x = -8.062257748

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + x = -8.062257748 + 1

Combine like terms: -1 + 1 = 0
0 + x = -8.062257748 + 1
x = -8.062257748 + 1

Combine like terms: -8.062257748 + 1 = -7.062257748
x = -7.062257748

Simplifying
x = -7.062257748

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.062257748, -7.062257748}
Solution
x = {0, 9.062257748, -7.062257748}