6x(3x+-6)=26

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

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

Reorder the terms:
6x(-6 + 3x) = 26
(-6 * 6x + 3x * 6x) = 26
(-36x + 18x2) = 26

Solving
-36x + 18x2 = 26

Solving for variable 'x'.

Reorder the terms:
-26 + -36x + 18x2 = 26 + -26

Combine like terms: 26 + -26 = 0
-26 + -36x + 18x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-13 + -18x + 9x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-13 + -18x + 9x2)' equal to zero and attempt to solve:

Simplifying
-13 + -18x + 9x2 = 0

Solving
-13 + -18x + 9x2 = 0

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

Divide each side by '9'.
-1.444444444 + -2x + x2 = 0

Move the constant term to the right:

Add '1.444444444' to each side of the equation.
-1.444444444 + -2x + 1.444444444 + x2 = 0 + 1.444444444

Reorder the terms:
-1.444444444 + 1.444444444 + -2x + x2 = 0 + 1.444444444

Combine like terms: -1.444444444 + 1.444444444 = 0.000000000
0.000000000 + -2x + x2 = 0 + 1.444444444
-2x + x2 = 0 + 1.444444444

Combine like terms: 0 + 1.444444444 = 1.444444444
-2x + x2 = 1.444444444

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 1.444444444 + 1

Reorder the terms:
1 + -2x + x2 = 1.444444444 + 1

Combine like terms: 1.444444444 + 1 = 2.444444444
1 + -2x + x2 = 2.444444444

Factor a perfect square on the left side:
(x + -1)(x + -1) = 2.444444444

Calculate the square root of the right side: 1.56347192

Break this problem into two subproblems by setting 
(x + -1) equal to 1.56347192 and -1.56347192.

Subproblem 1
x + -1 = 1.56347192

Simplifying
x + -1 = 1.56347192

Reorder the terms:
-1 + x = 1.56347192

Solving
-1 + x = 1.56347192

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 1.56347192 + 1

Combine like terms: -1 + 1 = 0
0 + x = 1.56347192 + 1
x = 1.56347192 + 1

Combine like terms: 1.56347192 + 1 = 2.56347192
x = 2.56347192

Simplifying
x = 2.56347192

Subproblem 2
x + -1 = -1.56347192

Simplifying
x + -1 = -1.56347192

Reorder the terms:
-1 + x = -1.56347192

Solving
-1 + x = -1.56347192

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -1.56347192 + 1

Combine like terms: -1 + 1 = 0
0 + x = -1.56347192 + 1
x = -1.56347192 + 1

Combine like terms: -1.56347192 + 1 = -0.56347192
x = -0.56347192

Simplifying
x = -0.56347192

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.56347192, -0.56347192}
Solution
x = {2.56347192, -0.56347192}