6u^2=12u+10

Solution for 6u^2=12u+10 equation:

Simplifying
6u2 = 12u + 10

Reorder the terms:
6u2 = 10 + 12u

Solving
6u2 = 10 + 12u

Solving for variable 'u'.

Reorder the terms:
-10 + -12u + 6u2 = 10 + 12u + -10 + -12u

Reorder the terms:
-10 + -12u + 6u2 = 10 + -10 + 12u + -12u

Combine like terms: 10 + -10 = 0
-10 + -12u + 6u2 = 0 + 12u + -12u
-10 + -12u + 6u2 = 12u + -12u

Combine like terms: 12u + -12u = 0
-10 + -12u + 6u2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + -6u + 3u2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + -6u + 3u2)' equal to zero and attempt to solve:

Simplifying
-5 + -6u + 3u2 = 0

Solving
-5 + -6u + 3u2 = 0

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

Divide each side by '3'.
-1.666666667 + -2u + u2 = 0

Move the constant term to the right:

Add '1.666666667' to each side of the equation.
-1.666666667 + -2u + 1.666666667 + u2 = 0 + 1.666666667

Reorder the terms:
-1.666666667 + 1.666666667 + -2u + u2 = 0 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + -2u + u2 = 0 + 1.666666667
-2u + u2 = 0 + 1.666666667

Combine like terms: 0 + 1.666666667 = 1.666666667
-2u + u2 = 1.666666667

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

Add '1' to each side of the equation.
-2u + 1 + u2 = 1.666666667 + 1

Reorder the terms:
1 + -2u + u2 = 1.666666667 + 1

Combine like terms: 1.666666667 + 1 = 2.666666667
1 + -2u + u2 = 2.666666667

Factor a perfect square on the left side:
(u + -1)(u + -1) = 2.666666667

Calculate the square root of the right side: 1.632993162

Break this problem into two subproblems by setting 
(u + -1) equal to 1.632993162 and -1.632993162.

Subproblem 1
u + -1 = 1.632993162

Simplifying
u + -1 = 1.632993162

Reorder the terms:
-1 + u = 1.632993162

Solving
-1 + u = 1.632993162

Solving for variable 'u'.

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

Add '1' to each side of the equation.
-1 + 1 + u = 1.632993162 + 1

Combine like terms: -1 + 1 = 0
0 + u = 1.632993162 + 1
u = 1.632993162 + 1

Combine like terms: 1.632993162 + 1 = 2.632993162
u = 2.632993162

Simplifying
u = 2.632993162

Subproblem 2
u + -1 = -1.632993162

Simplifying
u + -1 = -1.632993162

Reorder the terms:
-1 + u = -1.632993162

Solving
-1 + u = -1.632993162

Solving for variable 'u'.

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

Add '1' to each side of the equation.
-1 + 1 + u = -1.632993162 + 1

Combine like terms: -1 + 1 = 0
0 + u = -1.632993162 + 1
u = -1.632993162 + 1

Combine like terms: -1.632993162 + 1 = -0.632993162
u = -0.632993162

Simplifying
u = -0.632993162

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {2.632993162, -0.632993162}
Solution
u = {2.632993162, -0.632993162}