6(3x-1)-2x=2(2x-5)x

Solution for 6(3x-1)-2x=2(2x-5)x equation:

Simplifying
6(3x + -1) + -2x = 2(2x + -5) * x

Reorder the terms:
6(-1 + 3x) + -2x = 2(2x + -5) * x
(-1 * 6 + 3x * 6) + -2x = 2(2x + -5) * x
(-6 + 18x) + -2x = 2(2x + -5) * x

Combine like terms: 18x + -2x = 16x
-6 + 16x = 2(2x + -5) * x

Reorder the terms:
-6 + 16x = 2(-5 + 2x) * x

Reorder the terms for easier multiplication:
-6 + 16x = 2x(-5 + 2x)
-6 + 16x = (-5 * 2x + 2x * 2x)
-6 + 16x = (-10x + 4x2)

Solving
-6 + 16x = -10x + 4x2

Solving for variable 'x'.

Combine like terms: 16x + 10x = 26x
-6 + 26x + -4x2 = -10x + 4x2 + 10x + -4x2

Reorder the terms:
-6 + 26x + -4x2 = -10x + 10x + 4x2 + -4x2

Combine like terms: -10x + 10x = 0
-6 + 26x + -4x2 = 0 + 4x2 + -4x2
-6 + 26x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-6 + 26x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + 13x + -2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + 13x + -2x2)' equal to zero and attempt to solve:

Simplifying
-3 + 13x + -2x2 = 0

Solving
-3 + 13x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
1.5 + -6.5x + x2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + -6.5x + -1.5 + x2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + -6.5x + x2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + -6.5x + x2 = 0 + -1.5
-6.5x + x2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
-6.5x + x2 = -1.5

The x term is -6.5x.  Take half its coefficient (-3.25).
Square it (10.5625) and add it to both sides.

Add '10.5625' to each side of the equation.
-6.5x + 10.5625 + x2 = -1.5 + 10.5625

Reorder the terms:
10.5625 + -6.5x + x2 = -1.5 + 10.5625

Combine like terms: -1.5 + 10.5625 = 9.0625
10.5625 + -6.5x + x2 = 9.0625

Factor a perfect square on the left side:
(x + -3.25)(x + -3.25) = 9.0625

Calculate the square root of the right side: 3.010398645

Break this problem into two subproblems by setting 
(x + -3.25) equal to 3.010398645 and -3.010398645.

Subproblem 1
x + -3.25 = 3.010398645

Simplifying
x + -3.25 = 3.010398645

Reorder the terms:
-3.25 + x = 3.010398645

Solving
-3.25 + x = 3.010398645

Solving for variable 'x'.

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

Add '3.25' to each side of the equation.
-3.25 + 3.25 + x = 3.010398645 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + x = 3.010398645 + 3.25
x = 3.010398645 + 3.25

Combine like terms: 3.010398645 + 3.25 = 6.260398645
x = 6.260398645

Simplifying
x = 6.260398645

Subproblem 2
x + -3.25 = -3.010398645

Simplifying
x + -3.25 = -3.010398645

Reorder the terms:
-3.25 + x = -3.010398645

Solving
-3.25 + x = -3.010398645

Solving for variable 'x'.

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

Add '3.25' to each side of the equation.
-3.25 + 3.25 + x = -3.010398645 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + x = -3.010398645 + 3.25
x = -3.010398645 + 3.25

Combine like terms: -3.010398645 + 3.25 = 0.239601355
x = 0.239601355

Simplifying
x = 0.239601355

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.260398645, 0.239601355}
Solution
x = {6.260398645, 0.239601355}