6x(x-1)=26

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Solution for 6x(x-1)=26 equation: 


Simplifying
6x(x + -1) = 26

Reorder the terms:
6x(-1 + x) = 26
(-1 * 6x + x * 6x) = 26
(-6x + 6x2) = 26

Solving
-6x + 6x2 = 26

Solving for variable 'x'.

Reorder the terms:
-26 + -6x + 6x2 = 26 + -26

Combine like terms: 26 + -26 = 0
-26 + -6x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-13 + -3x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-13 + -3x + 3x2)' equal to zero and attempt to solve:

Simplifying
-13 + -3x + 3x2 = 0

Solving
-13 + -3x + 3x2 = 0

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

Divide each side by '3'.
-4.333333333 + -1x + x2 = 0

Move the constant term to the right:

Add '4.333333333' to each side of the equation.
-4.333333333 + -1x + 4.333333333 + x2 = 0 + 4.333333333

Reorder the terms:
-4.333333333 + 4.333333333 + -1x + x2 = 0 + 4.333333333

Combine like terms: -4.333333333 + 4.333333333 = 0.000000000
0.000000000 + -1x + x2 = 0 + 4.333333333
-1x + x2 = 0 + 4.333333333

Combine like terms: 0 + 4.333333333 = 4.333333333
-1x + x2 = 4.333333333

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 4.333333333 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 4.333333333 + 0.25

Combine like terms: 4.333333333 + 0.25 = 4.583333333
0.25 + -1x + x2 = 4.583333333

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 4.583333333

Calculate the square root of the right side: 2.140872096

Break this problem into two subproblems by setting 
(x + -0.5) equal to 2.140872096 and -2.140872096.


Subproblem 1
x + -0.5 = 2.140872096

Simplifying
x + -0.5 = 2.140872096

Reorder the terms:
-0.5 + x = 2.140872096

Solving
-0.5 + x = 2.140872096

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = 2.140872096 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 2.140872096 + 0.5
x = 2.140872096 + 0.5

Combine like terms: 2.140872096 + 0.5 = 2.640872096
x = 2.640872096

Simplifying
x = 2.640872096


Subproblem 2
x + -0.5 = -2.140872096

Simplifying
x + -0.5 = -2.140872096

Reorder the terms:
-0.5 + x = -2.140872096

Solving
-0.5 + x = -2.140872096

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = -2.140872096 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -2.140872096 + 0.5
x = -2.140872096 + 0.5

Combine like terms: -2.140872096 + 0.5 = -1.640872096
x = -1.640872096

Simplifying
x = -1.640872096


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.640872096, -1.640872096}
Solution
x = {2.640872096, -1.640872096}

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