(2x-6)+(x+3)(2x-6)+(x+3)=26

Solution for (2x-6)+(x+3)(2x-6)+(x+3)=26 equation:

Simplifying
(2x + -6) + (x + 3)(2x + -6) + (x + 3) = 26

Reorder the terms:
(-6 + 2x) + (x + 3)(2x + -6) + (x + 3) = 26

Remove parenthesis around (-6 + 2x)
-6 + 2x + (x + 3)(2x + -6) + (x + 3) = 26

Reorder the terms:
-6 + 2x + (3 + x)(2x + -6) + (x + 3) = 26

Reorder the terms:
-6 + 2x + (3 + x)(-6 + 2x) + (x + 3) = 26

Multiply (3 + x) * (-6 + 2x)
-6 + 2x + (3(-6 + 2x) + x(-6 + 2x)) + (x + 3) = 26
-6 + 2x + ((-6 * 3 + 2x * 3) + x(-6 + 2x)) + (x + 3) = 26
-6 + 2x + ((-18 + 6x) + x(-6 + 2x)) + (x + 3) = 26
-6 + 2x + (-18 + 6x + (-6 * x + 2x * x)) + (x + 3) = 26
-6 + 2x + (-18 + 6x + (-6x + 2x2)) + (x + 3) = 26

Combine like terms: 6x + -6x = 0
-6 + 2x + (-18 + 0 + 2x2) + (x + 3) = 26
-6 + 2x + (-18 + 2x2) + (x + 3) = 26

Reorder the terms:
-6 + 2x + -18 + 2x2 + (3 + x) = 26

Remove parenthesis around (3 + x)
-6 + 2x + -18 + 2x2 + 3 + x = 26

Reorder the terms:
-6 + -18 + 3 + 2x + x + 2x2 = 26

Combine like terms: -6 + -18 = -24
-24 + 3 + 2x + x + 2x2 = 26

Combine like terms: -24 + 3 = -21
-21 + 2x + x + 2x2 = 26

Combine like terms: 2x + x = 3x
-21 + 3x + 2x2 = 26

Solving
-21 + 3x + 2x2 = 26

Solving for variable 'x'.

Reorder the terms:
-21 + -26 + 3x + 2x2 = 26 + -26

Combine like terms: -21 + -26 = -47
-47 + 3x + 2x2 = 26 + -26

Combine like terms: 26 + -26 = 0
-47 + 3x + 2x2 = 0

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

Divide each side by '2'.
-23.5 + 1.5x + x2 = 0

Move the constant term to the right:

Add '23.5' to each side of the equation.
-23.5 + 1.5x + 23.5 + x2 = 0 + 23.5

Reorder the terms:
-23.5 + 23.5 + 1.5x + x2 = 0 + 23.5

Combine like terms: -23.5 + 23.5 = 0.0
0.0 + 1.5x + x2 = 0 + 23.5
1.5x + x2 = 0 + 23.5

Combine like terms: 0 + 23.5 = 23.5
1.5x + x2 = 23.5

The x term is 1.5x.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5x + 0.5625 + x2 = 23.5 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = 23.5 + 0.5625

Combine like terms: 23.5 + 0.5625 = 24.0625
0.5625 + 1.5x + x2 = 24.0625

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = 24.0625

Calculate the square root of the right side: 4.905354218

Break this problem into two subproblems by setting 
(x + 0.75) equal to 4.905354218 and -4.905354218.

Subproblem 1
x + 0.75 = 4.905354218

Simplifying
x + 0.75 = 4.905354218

Reorder the terms:
0.75 + x = 4.905354218

Solving
0.75 + x = 4.905354218

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = 4.905354218 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = 4.905354218 + -0.75
x = 4.905354218 + -0.75

Combine like terms: 4.905354218 + -0.75 = 4.155354218
x = 4.155354218

Simplifying
x = 4.155354218

Subproblem 2
x + 0.75 = -4.905354218

Simplifying
x + 0.75 = -4.905354218

Reorder the terms:
0.75 + x = -4.905354218

Solving
0.75 + x = -4.905354218

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = -4.905354218 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = -4.905354218 + -0.75
x = -4.905354218 + -0.75

Combine like terms: -4.905354218 + -0.75 = -5.655354218
x = -5.655354218

Simplifying
x = -5.655354218

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.155354218, -5.655354218}