2v^2-6=2v+6

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

Simplifying
2v2 + -6 = 2v + 6

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

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

Solving
-6 + 2v2 = 6 + 2v

Solving for variable 'v'.

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

Combine like terms: -6 + -6 = -12
-12 + -2v + 2v2 = 6 + 2v + -6 + -2v

Reorder the terms:
-12 + -2v + 2v2 = 6 + -6 + 2v + -2v

Combine like terms: 6 + -6 = 0
-12 + -2v + 2v2 = 0 + 2v + -2v
-12 + -2v + 2v2 = 2v + -2v

Combine like terms: 2v + -2v = 0
-12 + -2v + 2v2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + -1v + v2) = 0

Factor a trinomial.
2((-2 + -1v)(3 + -1v)) = 0

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

Simplifying
-2 + -1v = 0

Solving
-2 + -1v = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1v = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1v = 0 + 2
-1v = 0 + 2

Combine like terms: 0 + 2 = 2
-1v = 2

Divide each side by '-1'.
v = -2

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

Simplifying
3 + -1v = 0

Solving
3 + -1v = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1v = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1v = 0 + -3
-1v = 0 + -3

Combine like terms: 0 + -3 = -3
-1v = -3

Divide each side by '-1'.
v = 3

Simplifying
v = 3
Solution
v = {-2, 3}