20x^3-36x^2+12x=0

Solution for 20x^3-36x^2+12x=0 equation:

Simplifying
20x3 + -36x2 + 12x = 0

Reorder the terms:
12x + -36x2 + 20x3 = 0

Solving
12x + -36x2 + 20x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(3 + -9x + 5x2) = 0

Ignore the factor 4.
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 '(3 + -9x + 5x2)' equal to zero and attempt to solve:

Simplifying
3 + -9x + 5x2 = 0

Solving
3 + -9x + 5x2 = 0

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
0.6 + -1.8x + x2 = 0

Move the constant term to the right:

Add '-0.6' to each side of the equation.
0.6 + -1.8x + -0.6 + x2 = 0 + -0.6

Reorder the terms:
0.6 + -0.6 + -1.8x + x2 = 0 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + -1.8x + x2 = 0 + -0.6
-1.8x + x2 = 0 + -0.6

Combine like terms: 0 + -0.6 = -0.6
-1.8x + x2 = -0.6

The x term is -1.8x.  Take half its coefficient (-0.9).
Square it (0.81) and add it to both sides.

Add '0.81' to each side of the equation.
-1.8x + 0.81 + x2 = -0.6 + 0.81

Reorder the terms:
0.81 + -1.8x + x2 = -0.6 + 0.81

Combine like terms: -0.6 + 0.81 = 0.21
0.81 + -1.8x + x2 = 0.21

Factor a perfect square on the left side:
(x + -0.9)(x + -0.9) = 0.21

Calculate the square root of the right side: 0.458257569

Break this problem into two subproblems by setting 
(x + -0.9) equal to 0.458257569 and -0.458257569.

Subproblem 1
x + -0.9 = 0.458257569

Simplifying
x + -0.9 = 0.458257569

Reorder the terms:
-0.9 + x = 0.458257569

Solving
-0.9 + x = 0.458257569

Solving for variable 'x'.

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

Add '0.9' to each side of the equation.
-0.9 + 0.9 + x = 0.458257569 + 0.9

Combine like terms: -0.9 + 0.9 = 0.0
0.0 + x = 0.458257569 + 0.9
x = 0.458257569 + 0.9

Combine like terms: 0.458257569 + 0.9 = 1.358257569
x = 1.358257569

Simplifying
x = 1.358257569

Subproblem 2
x + -0.9 = -0.458257569

Simplifying
x + -0.9 = -0.458257569

Reorder the terms:
-0.9 + x = -0.458257569

Solving
-0.9 + x = -0.458257569

Solving for variable 'x'.

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

Add '0.9' to each side of the equation.
-0.9 + 0.9 + x = -0.458257569 + 0.9

Combine like terms: -0.9 + 0.9 = 0.0
0.0 + x = -0.458257569 + 0.9
x = -0.458257569 + 0.9

Combine like terms: -0.458257569 + 0.9 = 0.441742431
x = 0.441742431

Simplifying
x = 0.441742431

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.358257569, 0.441742431}
Solution
x = {0, 1.358257569, 0.441742431}