3v^2+v=2

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

Simplifying
3v2 + v = 2

Reorder the terms:
v + 3v2 = 2

Solving
v + 3v2 = 2

Solving for variable 'v'.

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

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

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

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

Simplifying
-1 + -1v = 0

Solving
-1 + -1v = 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 + -1v = 0 + 1

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

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

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

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

Simplifying
2 + -3v = 0

Solving
2 + -3v = 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 + -3v = 0 + -2

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

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

Divide each side by '-3'.
v = 0.6666666667

Simplifying
v = 0.6666666667
Solution
v = {-1, 0.6666666667}