3v=2v^2-2

Solution for 3v=2v^2-2 equation:

Simplifying
3v = 2v2 + -2

Reorder the terms:
3v = -2 + 2v2

Solving
3v = -2 + 2v2

Solving for variable 'v'.

Reorder the terms:
2 + 3v + -2v2 = -2 + 2v2 + 2 + -2v2

Reorder the terms:
2 + 3v + -2v2 = -2 + 2 + 2v2 + -2v2

Combine like terms: -2 + 2 = 0
2 + 3v + -2v2 = 0 + 2v2 + -2v2
2 + 3v + -2v2 = 2v2 + -2v2

Combine like terms: 2v2 + -2v2 = 0
2 + 3v + -2v2 = 0

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

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 '(1 + 2v)' equal to zero and attempt to solve:

Simplifying
1 + 2v = 0

Solving
1 + 2v = 0

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

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

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

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

Divide each side by '2'.
v = -0.5

Simplifying
v = -0.5
Solution
v = {2, -0.5}