6v^2=6-2v

Solution for 6v^2=6-2v equation:

Simplifying
6v2 = 6 + -2v

Solving
6v2 = 6 + -2v

Solving for variable 'v'.

Reorder the terms:
-6 + 2v + 6v2 = 6 + -2v + -6 + 2v

Reorder the terms:
-6 + 2v + 6v2 = 6 + -6 + -2v + 2v

Combine like terms: 6 + -6 = 0
-6 + 2v + 6v2 = 0 + -2v + 2v
-6 + 2v + 6v2 = -2v + 2v

Combine like terms: -2v + 2v = 0
-6 + 2v + 6v2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + v + 3v2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + v + 3v2)' equal to zero and attempt to solve:

Simplifying
-3 + v + 3v2 = 0

Solving
-3 + v + 3v2 = 0

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

Divide each side by '3'.
-1 + 0.3333333333v + v2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 0.3333333333v + 1 + v2 = 0 + 1

Reorder the terms:
-1 + 1 + 0.3333333333v + v2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 0.3333333333v + v2 = 0 + 1
0.3333333333v + v2 = 0 + 1

Combine like terms: 0 + 1 = 1
0.3333333333v + v2 = 1

The v term is v.  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.
0.3333333333v + 0.25 + v2 = 1 + 0.25

Reorder the terms:
0.25 + 0.3333333333v + v2 = 1 + 0.25

Combine like terms: 1 + 0.25 = 1.25
0.25 + 0.3333333333v + v2 = 1.25

Factor a perfect square on the left side:
(v + 0.5)(v + 0.5) = 1.25

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(v + 0.5) equal to 1.118033989 and -1.118033989.

Subproblem 1
v + 0.5 = 1.118033989

Simplifying
v + 0.5 = 1.118033989

Reorder the terms:
0.5 + v = 1.118033989

Solving
0.5 + v = 1.118033989

Solving for variable 'v'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + v = 1.118033989 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + v = 1.118033989 + -0.5
v = 1.118033989 + -0.5

Combine like terms: 1.118033989 + -0.5 = 0.618033989
v = 0.618033989

Simplifying
v = 0.618033989

Subproblem 2
v + 0.5 = -1.118033989

Simplifying
v + 0.5 = -1.118033989

Reorder the terms:
0.5 + v = -1.118033989

Solving
0.5 + v = -1.118033989

Solving for variable 'v'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + v = -1.118033989 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + v = -1.118033989 + -0.5
v = -1.118033989 + -0.5

Combine like terms: -1.118033989 + -0.5 = -1.618033989
v = -1.618033989

Simplifying
v = -1.618033989

Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {0.618033989, -1.618033989}
Solution
v = {0.618033989, -1.618033989}