-6u^2+6=3u

Solution for -6u^2+6=3u equation:

Simplifying
-6u2 + 6 = 3u

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

Solving
6 + -6u2 = 3u

Solving for variable 'u'.

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

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

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

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

Simplifying
2 + -1u + -2u2 = 0

Solving
2 + -1u + -2u2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-1 + 0.5u + u2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 0.5u + 1 + u2 = 0 + 1

Reorder the terms:
-1 + 1 + 0.5u + u2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 0.5u + u2 = 0 + 1
0.5u + u2 = 0 + 1

Combine like terms: 0 + 1 = 1
0.5u + u2 = 1

The u term is 0.5u.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5u + 0.0625 + u2 = 1 + 0.0625

Reorder the terms:
0.0625 + 0.5u + u2 = 1 + 0.0625

Combine like terms: 1 + 0.0625 = 1.0625
0.0625 + 0.5u + u2 = 1.0625

Factor a perfect square on the left side:
(u + 0.25)(u + 0.25) = 1.0625

Calculate the square root of the right side: 1.030776406

Break this problem into two subproblems by setting 
(u + 0.25) equal to 1.030776406 and -1.030776406.

Subproblem 1
u + 0.25 = 1.030776406

Simplifying
u + 0.25 = 1.030776406

Reorder the terms:
0.25 + u = 1.030776406

Solving
0.25 + u = 1.030776406

Solving for variable 'u'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + u = 1.030776406 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + u = 1.030776406 + -0.25
u = 1.030776406 + -0.25

Combine like terms: 1.030776406 + -0.25 = 0.780776406
u = 0.780776406

Simplifying
u = 0.780776406

Subproblem 2
u + 0.25 = -1.030776406

Simplifying
u + 0.25 = -1.030776406

Reorder the terms:
0.25 + u = -1.030776406

Solving
0.25 + u = -1.030776406

Solving for variable 'u'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + u = -1.030776406 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + u = -1.030776406 + -0.25
u = -1.030776406 + -0.25

Combine like terms: -1.030776406 + -0.25 = -1.280776406
u = -1.280776406

Simplifying
u = -1.280776406

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {0.780776406, -1.280776406}
Solution
u = {0.780776406, -1.280776406}