6x^3-22x^2-20x=0

Solution for 6x^3-22x^2-20x=0 equation:

Simplifying
6x3 + -22x2 + -20x = 0

Reorder the terms:
-20x + -22x2 + 6x3 = 0

Solving
-20x + -22x2 + 6x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-10 + -11x + 3x2) = 0

Ignore the factor 2.
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 '(-10 + -11x + 3x2)' equal to zero and attempt to solve:

Simplifying
-10 + -11x + 3x2 = 0

Solving
-10 + -11x + 3x2 = 0

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

Divide each side by '3'.
-3.333333333 + -3.666666667x + x2 = 0

Move the constant term to the right:

Add '3.333333333' to each side of the equation.
-3.333333333 + -3.666666667x + 3.333333333 + x2 = 0 + 3.333333333

Reorder the terms:
-3.333333333 + 3.333333333 + -3.666666667x + x2 = 0 + 3.333333333

Combine like terms: -3.333333333 + 3.333333333 = 0.000000000
0.000000000 + -3.666666667x + x2 = 0 + 3.333333333
-3.666666667x + x2 = 0 + 3.333333333

Combine like terms: 0 + 3.333333333 = 3.333333333
-3.666666667x + x2 = 3.333333333

The x term is -3.666666667x.  Take half its coefficient (-1.833333334).
Square it (3.361111114) and add it to both sides.

Add '3.361111114' to each side of the equation.
-3.666666667x + 3.361111114 + x2 = 3.333333333 + 3.361111114

Reorder the terms:
3.361111114 + -3.666666667x + x2 = 3.333333333 + 3.361111114

Combine like terms: 3.333333333 + 3.361111114 = 6.694444447
3.361111114 + -3.666666667x + x2 = 6.694444447

Factor a perfect square on the left side:
(x + -1.833333334)(x + -1.833333334) = 6.694444447

Calculate the square root of the right side: 2.58736245

Break this problem into two subproblems by setting 
(x + -1.833333334) equal to 2.58736245 and -2.58736245.

Subproblem 1
x + -1.833333334 = 2.58736245

Simplifying
x + -1.833333334 = 2.58736245

Reorder the terms:
-1.833333334 + x = 2.58736245

Solving
-1.833333334 + x = 2.58736245

Solving for variable 'x'.

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

Add '1.833333334' to each side of the equation.
-1.833333334 + 1.833333334 + x = 2.58736245 + 1.833333334

Combine like terms: -1.833333334 + 1.833333334 = 0.000000000
0.000000000 + x = 2.58736245 + 1.833333334
x = 2.58736245 + 1.833333334

Combine like terms: 2.58736245 + 1.833333334 = 4.420695784
x = 4.420695784

Simplifying
x = 4.420695784

Subproblem 2
x + -1.833333334 = -2.58736245

Simplifying
x + -1.833333334 = -2.58736245

Reorder the terms:
-1.833333334 + x = -2.58736245

Solving
-1.833333334 + x = -2.58736245

Solving for variable 'x'.

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

Add '1.833333334' to each side of the equation.
-1.833333334 + 1.833333334 + x = -2.58736245 + 1.833333334

Combine like terms: -1.833333334 + 1.833333334 = 0.000000000
0.000000000 + x = -2.58736245 + 1.833333334
x = -2.58736245 + 1.833333334

Combine like terms: -2.58736245 + 1.833333334 = -0.754029116
x = -0.754029116

Simplifying
x = -0.754029116

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.420695784, -0.754029116}
Solution
x = {0, 4.420695784, -0.754029116}