12u-6-2u^2=0

Solution for 12u-6-2u^2=0 equation:

Simplifying
12u + -6 + -2u2 = 0

Reorder the terms:
-6 + 12u + -2u2 = 0

Solving
-6 + 12u + -2u2 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + 6u + -1u2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + 6u + -1u2)' equal to zero and attempt to solve:

Simplifying
-3 + 6u + -1u2 = 0

Solving
-3 + 6u + -1u2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
3 + -6u + u2 = 0

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -6u + -3 + u2 = 0 + -3

Reorder the terms:
3 + -3 + -6u + u2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -6u + u2 = 0 + -3
-6u + u2 = 0 + -3

Combine like terms: 0 + -3 = -3
-6u + u2 = -3

The u term is -6u.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6u + 9 + u2 = -3 + 9

Reorder the terms:
9 + -6u + u2 = -3 + 9

Combine like terms: -3 + 9 = 6
9 + -6u + u2 = 6

Factor a perfect square on the left side:
(u + -3)(u + -3) = 6

Calculate the square root of the right side: 2.449489743

Break this problem into two subproblems by setting 
(u + -3) equal to 2.449489743 and -2.449489743.

Subproblem 1
u + -3 = 2.449489743

Simplifying
u + -3 = 2.449489743

Reorder the terms:
-3 + u = 2.449489743

Solving
-3 + u = 2.449489743

Solving for variable 'u'.

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

Add '3' to each side of the equation.
-3 + 3 + u = 2.449489743 + 3

Combine like terms: -3 + 3 = 0
0 + u = 2.449489743 + 3
u = 2.449489743 + 3

Combine like terms: 2.449489743 + 3 = 5.449489743
u = 5.449489743

Simplifying
u = 5.449489743

Subproblem 2
u + -3 = -2.449489743

Simplifying
u + -3 = -2.449489743

Reorder the terms:
-3 + u = -2.449489743

Solving
-3 + u = -2.449489743

Solving for variable 'u'.

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

Add '3' to each side of the equation.
-3 + 3 + u = -2.449489743 + 3

Combine like terms: -3 + 3 = 0
0 + u = -2.449489743 + 3
u = -2.449489743 + 3

Combine like terms: -2.449489743 + 3 = 0.550510257
u = 0.550510257

Simplifying
u = 0.550510257

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {5.449489743, 0.550510257}
Solution
u = {5.449489743, 0.550510257}