6x(x-1)-2x=38

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Solution for 6x(x-1)-2x=38 equation: 


Simplifying
6x(x + -1) + -2x = 38

Reorder the terms:
6x(-1 + x) + -2x = 38
(-1 * 6x + x * 6x) + -2x = 38
(-6x + 6x2) + -2x = 38

Reorder the terms:
-6x + -2x + 6x2 = 38

Combine like terms: -6x + -2x = -8x
-8x + 6x2 = 38

Solving
-8x + 6x2 = 38

Solving for variable 'x'.

Reorder the terms:
-38 + -8x + 6x2 = 38 + -38

Combine like terms: 38 + -38 = 0
-38 + -8x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-19 + -4x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-19 + -4x + 3x2)' equal to zero and attempt to solve:

Simplifying
-19 + -4x + 3x2 = 0

Solving
-19 + -4x + 3x2 = 0

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

Divide each side by '3'.
-6.333333333 + -1.333333333x + x2 = 0

Move the constant term to the right:

Add '6.333333333' to each side of the equation.
-6.333333333 + -1.333333333x + 6.333333333 + x2 = 0 + 6.333333333

Reorder the terms:
-6.333333333 + 6.333333333 + -1.333333333x + x2 = 0 + 6.333333333

Combine like terms: -6.333333333 + 6.333333333 = 0.000000000
0.000000000 + -1.333333333x + x2 = 0 + 6.333333333
-1.333333333x + x2 = 0 + 6.333333333

Combine like terms: 0 + 6.333333333 = 6.333333333
-1.333333333x + x2 = 6.333333333

The x term is -1.333333333x.  Take half its coefficient (-0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
-1.333333333x + 0.4444444442 + x2 = 6.333333333 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333x + x2 = 6.333333333 + 0.4444444442

Combine like terms: 6.333333333 + 0.4444444442 = 6.7777777772
0.4444444442 + -1.333333333x + x2 = 6.7777777772

Factor a perfect square on the left side:
(x + -0.6666666665)(x + -0.6666666665) = 6.7777777772

Calculate the square root of the right side: 2.603416559

Break this problem into two subproblems by setting 
(x + -0.6666666665) equal to 2.603416559 and -2.603416559.


Subproblem 1
x + -0.6666666665 = 2.603416559

Simplifying
x + -0.6666666665 = 2.603416559

Reorder the terms:
-0.6666666665 + x = 2.603416559

Solving
-0.6666666665 + x = 2.603416559

Solving for variable 'x'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + x = 2.603416559 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + x = 2.603416559 + 0.6666666665
x = 2.603416559 + 0.6666666665

Combine like terms: 2.603416559 + 0.6666666665 = 3.2700832255
x = 3.2700832255

Simplifying
x = 3.2700832255


Subproblem 2
x + -0.6666666665 = -2.603416559

Simplifying
x + -0.6666666665 = -2.603416559

Reorder the terms:
-0.6666666665 + x = -2.603416559

Solving
-0.6666666665 + x = -2.603416559

Solving for variable 'x'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + x = -2.603416559 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + x = -2.603416559 + 0.6666666665
x = -2.603416559 + 0.6666666665

Combine like terms: -2.603416559 + 0.6666666665 = -1.9367498925
x = -1.9367498925

Simplifying
x = -1.9367498925


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.2700832255, -1.9367498925}
Solution
x = {3.2700832255, -1.9367498925}

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