(x-2)(6x-4)=12

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Solution for (x-2)(6x-4)=12 equation: 


Simplifying
(x + -2)(6x + -4) = 12

Reorder the terms:
(-2 + x)(6x + -4) = 12

Reorder the terms:
(-2 + x)(-4 + 6x) = 12

Multiply (-2 + x) * (-4 + 6x)
(-2(-4 + 6x) + x(-4 + 6x)) = 12
((-4 * -2 + 6x * -2) + x(-4 + 6x)) = 12
((8 + -12x) + x(-4 + 6x)) = 12
(8 + -12x + (-4 * x + 6x * x)) = 12
(8 + -12x + (-4x + 6x2)) = 12

Combine like terms: -12x + -4x = -16x
(8 + -16x + 6x2) = 12

Solving
8 + -16x + 6x2 = 12

Solving for variable 'x'.

Reorder the terms:
8 + -12 + -16x + 6x2 = 12 + -12

Combine like terms: 8 + -12 = -4
-4 + -16x + 6x2 = 12 + -12

Combine like terms: 12 + -12 = 0
-4 + -16x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + -8x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-2 + -8x + 3x2)' equal to zero and attempt to solve:

Simplifying
-2 + -8x + 3x2 = 0

Solving
-2 + -8x + 3x2 = 0

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

Divide each side by '3'.
-0.6666666667 + -2.666666667x + x2 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + -2.666666667x + 0.6666666667 + x2 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + -2.666666667x + x2 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + -2.666666667x + x2 = 0 + 0.6666666667
-2.666666667x + x2 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
-2.666666667x + x2 = 0.6666666667

The x term is -2.666666667x.  Take half its coefficient (-1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
-2.666666667x + 1.777777780 + x2 = 0.6666666667 + 1.777777780

Reorder the terms:
1.777777780 + -2.666666667x + x2 = 0.6666666667 + 1.777777780

Combine like terms: 0.6666666667 + 1.777777780 = 2.4444444467
1.777777780 + -2.666666667x + x2 = 2.4444444467

Factor a perfect square on the left side:
(x + -1.333333334)(x + -1.333333334) = 2.4444444467

Calculate the square root of the right side: 1.563471921

Break this problem into two subproblems by setting 
(x + -1.333333334) equal to 1.563471921 and -1.563471921.


Subproblem 1
x + -1.333333334 = 1.563471921

Simplifying
x + -1.333333334 = 1.563471921

Reorder the terms:
-1.333333334 + x = 1.563471921

Solving
-1.333333334 + x = 1.563471921

Solving for variable 'x'.

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

Add '1.333333334' to each side of the equation.
-1.333333334 + 1.333333334 + x = 1.563471921 + 1.333333334

Combine like terms: -1.333333334 + 1.333333334 = 0.000000000
0.000000000 + x = 1.563471921 + 1.333333334
x = 1.563471921 + 1.333333334

Combine like terms: 1.563471921 + 1.333333334 = 2.896805255
x = 2.896805255

Simplifying
x = 2.896805255


Subproblem 2
x + -1.333333334 = -1.563471921

Simplifying
x + -1.333333334 = -1.563471921

Reorder the terms:
-1.333333334 + x = -1.563471921

Solving
-1.333333334 + x = -1.563471921

Solving for variable 'x'.

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

Add '1.333333334' to each side of the equation.
-1.333333334 + 1.333333334 + x = -1.563471921 + 1.333333334

Combine like terms: -1.333333334 + 1.333333334 = 0.000000000
0.000000000 + x = -1.563471921 + 1.333333334
x = -1.563471921 + 1.333333334

Combine like terms: -1.563471921 + 1.333333334 = -0.230138587
x = -0.230138587

Simplifying
x = -0.230138587


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.896805255, -0.230138587}
Solution
x = {2.896805255, -0.230138587}

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