x^2(x^3-2x^2-4x)=0

Solution for x^2(x^3-2x^2-4x)=0 equation:

Simplifying
x2(x3 + -2x2 + -4x) = 0

Reorder the terms:
x2(-4x + -2x2 + x3) = 0
(-4x * x2 + -2x2 * x2 + x3 * x2) = 0
(-4x3 + -2x4 + x5) = 0

Solving
-4x3 + -2x4 + x5 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x3'.
x3(-4 + -2x + x2) = 0

Subproblem 1
Set the factor 'x3' equal to zero and attempt to solve:

Simplifying
x3 = 0

Solving
x3 = 0

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

Simplifying
x3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(-4 + -2x + x2)' equal to zero and attempt to solve:

Simplifying
-4 + -2x + x2 = 0

Solving
-4 + -2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -2x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + -2x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -2x + x2 = 0 + 4
-2x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
-2x + x2 = 4

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 = 4 + 1

Reorder the terms:
1 + -2x + x2 = 4 + 1

Combine like terms: 4 + 1 = 5
1 + -2x + x2 = 5

Factor a perfect square on the left side:
(x + -1)(x + -1) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(x + -1) equal to 2.236067978 and -2.236067978.

Subproblem 1
x + -1 = 2.236067978

Simplifying
x + -1 = 2.236067978

Reorder the terms:
-1 + x = 2.236067978

Solving
-1 + x = 2.236067978

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 = 2.236067978 + 1

Combine like terms: -1 + 1 = 0
0 + x = 2.236067978 + 1
x = 2.236067978 + 1

Combine like terms: 2.236067978 + 1 = 3.236067978
x = 3.236067978

Simplifying
x = 3.236067978

Subproblem 2
x + -1 = -2.236067978

Simplifying
x + -1 = -2.236067978

Reorder the terms:
-1 + x = -2.236067978

Solving
-1 + x = -2.236067978

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 = -2.236067978 + 1

Combine like terms: -1 + 1 = 0
0 + x = -2.236067978 + 1
x = -2.236067978 + 1

Combine like terms: -2.236067978 + 1 = -1.236067978
x = -1.236067978

Simplifying
x = -1.236067978

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.236067978, -1.236067978}
Solution
x = {3.236067978, -1.236067978}