8(4u-1)-12u=11u(2u-6)

Solution for 8(4u-1)-12u=11u(2u-6) equation:

Simplifying
8(4u + -1) + -12u = 11u(2u + -6)

Reorder the terms:
8(-1 + 4u) + -12u = 11u(2u + -6)
(-1 * 8 + 4u * 8) + -12u = 11u(2u + -6)
(-8 + 32u) + -12u = 11u(2u + -6)

Combine like terms: 32u + -12u = 20u
-8 + 20u = 11u(2u + -6)

Reorder the terms:
-8 + 20u = 11u(-6 + 2u)
-8 + 20u = (-6 * 11u + 2u * 11u)
-8 + 20u = (-66u + 22u2)

Solving
-8 + 20u = -66u + 22u2

Solving for variable 'u'.

Combine like terms: 20u + 66u = 86u
-8 + 86u + -22u2 = -66u + 22u2 + 66u + -22u2

Reorder the terms:
-8 + 86u + -22u2 = -66u + 66u + 22u2 + -22u2

Combine like terms: -66u + 66u = 0
-8 + 86u + -22u2 = 0 + 22u2 + -22u2
-8 + 86u + -22u2 = 22u2 + -22u2

Combine like terms: 22u2 + -22u2 = 0
-8 + 86u + -22u2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + 43u + -11u2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-4 + 43u + -11u2)' equal to zero and attempt to solve:

Simplifying
-4 + 43u + -11u2 = 0

Solving
-4 + 43u + -11u2 = 0

Begin completing the square.  Divide all terms by
-11 the coefficient of the squared term: 

Divide each side by '-11'.
0.3636363636 + -3.909090909u + u2 = 0

Move the constant term to the right:

Add '-0.3636363636' to each side of the equation.
0.3636363636 + -3.909090909u + -0.3636363636 + u2 = 0 + -0.3636363636

Reorder the terms:
0.3636363636 + -0.3636363636 + -3.909090909u + u2 = 0 + -0.3636363636

Combine like terms: 0.3636363636 + -0.3636363636 = 0.0000000000
0.0000000000 + -3.909090909u + u2 = 0 + -0.3636363636
-3.909090909u + u2 = 0 + -0.3636363636

Combine like terms: 0 + -0.3636363636 = -0.3636363636
-3.909090909u + u2 = -0.3636363636

The u term is -3.909090909u.  Take half its coefficient (-1.954545455).
Square it (3.820247936) and add it to both sides.

Add '3.820247936' to each side of the equation.
-3.909090909u + 3.820247936 + u2 = -0.3636363636 + 3.820247936

Reorder the terms:
3.820247936 + -3.909090909u + u2 = -0.3636363636 + 3.820247936

Combine like terms: -0.3636363636 + 3.820247936 = 3.4566115724
3.820247936 + -3.909090909u + u2 = 3.4566115724

Factor a perfect square on the left side:
(u + -1.954545455)(u + -1.954545455) = 3.4566115724

Calculate the square root of the right side: 1.859196486

Break this problem into two subproblems by setting 
(u + -1.954545455) equal to 1.859196486 and -1.859196486.

Subproblem 1
u + -1.954545455 = 1.859196486

Simplifying
u + -1.954545455 = 1.859196486

Reorder the terms:
-1.954545455 + u = 1.859196486

Solving
-1.954545455 + u = 1.859196486

Solving for variable 'u'.

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

Add '1.954545455' to each side of the equation.
-1.954545455 + 1.954545455 + u = 1.859196486 + 1.954545455

Combine like terms: -1.954545455 + 1.954545455 = 0.000000000
0.000000000 + u = 1.859196486 + 1.954545455
u = 1.859196486 + 1.954545455

Combine like terms: 1.859196486 + 1.954545455 = 3.813741941
u = 3.813741941

Simplifying
u = 3.813741941

Subproblem 2
u + -1.954545455 = -1.859196486

Simplifying
u + -1.954545455 = -1.859196486

Reorder the terms:
-1.954545455 + u = -1.859196486

Solving
-1.954545455 + u = -1.859196486

Solving for variable 'u'.

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

Add '1.954545455' to each side of the equation.
-1.954545455 + 1.954545455 + u = -1.859196486 + 1.954545455

Combine like terms: -1.954545455 + 1.954545455 = 0.000000000
0.000000000 + u = -1.859196486 + 1.954545455
u = -1.859196486 + 1.954545455

Combine like terms: -1.859196486 + 1.954545455 = 0.095348969
u = 0.095348969

Simplifying
u = 0.095348969

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {3.813741941, 0.095348969}
Solution
u = {3.813741941, 0.095348969}