26-2(2x+2)=4(x+2)6x

Solution for 26-2(2x+2)=4(x+2)6x equation:

Simplifying
26 + -2(2x + 2) = 4(x + 2) * 6x

Reorder the terms:
26 + -2(2 + 2x) = 4(x + 2) * 6x
26 + (2 * -2 + 2x * -2) = 4(x + 2) * 6x
26 + (-4 + -4x) = 4(x + 2) * 6x

Combine like terms: 26 + -4 = 22
22 + -4x = 4(x + 2) * 6x

Reorder the terms:
22 + -4x = 4(2 + x) * 6x

Reorder the terms for easier multiplication:
22 + -4x = 4 * 6x(2 + x)

Multiply 4 * 6
22 + -4x = 24x(2 + x)
22 + -4x = (2 * 24x + x * 24x)
22 + -4x = (48x + 24x2)

Solving
22 + -4x = 48x + 24x2

Solving for variable 'x'.

Combine like terms: -4x + -48x = -52x
22 + -52x + -24x2 = 48x + 24x2 + -48x + -24x2

Reorder the terms:
22 + -52x + -24x2 = 48x + -48x + 24x2 + -24x2

Combine like terms: 48x + -48x = 0
22 + -52x + -24x2 = 0 + 24x2 + -24x2
22 + -52x + -24x2 = 24x2 + -24x2

Combine like terms: 24x2 + -24x2 = 0
22 + -52x + -24x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(11 + -26x + -12x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(11 + -26x + -12x2)' equal to zero and attempt to solve:

Simplifying
11 + -26x + -12x2 = 0

Solving
11 + -26x + -12x2 = 0

Begin completing the square.  Divide all terms by
-12 the coefficient of the squared term: 

Divide each side by '-12'.
-0.9166666667 + 2.166666667x + x2 = 0

Move the constant term to the right:

Add '0.9166666667' to each side of the equation.
-0.9166666667 + 2.166666667x + 0.9166666667 + x2 = 0 + 0.9166666667

Reorder the terms:
-0.9166666667 + 0.9166666667 + 2.166666667x + x2 = 0 + 0.9166666667

Combine like terms: -0.9166666667 + 0.9166666667 = 0.0000000000
0.0000000000 + 2.166666667x + x2 = 0 + 0.9166666667
2.166666667x + x2 = 0 + 0.9166666667

Combine like terms: 0 + 0.9166666667 = 0.9166666667
2.166666667x + x2 = 0.9166666667

The x term is 2.166666667x.  Take half its coefficient (1.083333334).
Square it (1.173611113) and add it to both sides.

Add '1.173611113' to each side of the equation.
2.166666667x + 1.173611113 + x2 = 0.9166666667 + 1.173611113

Reorder the terms:
1.173611113 + 2.166666667x + x2 = 0.9166666667 + 1.173611113

Combine like terms: 0.9166666667 + 1.173611113 = 2.0902777797
1.173611113 + 2.166666667x + x2 = 2.0902777797

Factor a perfect square on the left side:
(x + 1.083333334)(x + 1.083333334) = 2.0902777797

Calculate the square root of the right side: 1.445779298

Break this problem into two subproblems by setting 
(x + 1.083333334) equal to 1.445779298 and -1.445779298.

Subproblem 1
x + 1.083333334 = 1.445779298

Simplifying
x + 1.083333334 = 1.445779298

Reorder the terms:
1.083333334 + x = 1.445779298

Solving
1.083333334 + x = 1.445779298

Solving for variable 'x'.

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

Add '-1.083333334' to each side of the equation.
1.083333334 + -1.083333334 + x = 1.445779298 + -1.083333334

Combine like terms: 1.083333334 + -1.083333334 = 0.000000000
0.000000000 + x = 1.445779298 + -1.083333334
x = 1.445779298 + -1.083333334

Combine like terms: 1.445779298 + -1.083333334 = 0.362445964
x = 0.362445964

Simplifying
x = 0.362445964

Subproblem 2
x + 1.083333334 = -1.445779298

Simplifying
x + 1.083333334 = -1.445779298

Reorder the terms:
1.083333334 + x = -1.445779298

Solving
1.083333334 + x = -1.445779298

Solving for variable 'x'.

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

Add '-1.083333334' to each side of the equation.
1.083333334 + -1.083333334 + x = -1.445779298 + -1.083333334

Combine like terms: 1.083333334 + -1.083333334 = 0.000000000
0.000000000 + x = -1.445779298 + -1.083333334
x = -1.445779298 + -1.083333334

Combine like terms: -1.445779298 + -1.083333334 = -2.529112632
x = -2.529112632

Simplifying
x = -2.529112632

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.362445964, -2.529112632}
Solution
x = {0.362445964, -2.529112632}