3v^4+5v^2=2

Solution for 3v^4+5v^2=2 equation:

Simplifying
3v4 + 5v2 = 2

Reorder the terms:
5v2 + 3v4 = 2

Solving
5v2 + 3v4 = 2

Solving for variable 'v'.

Reorder the terms:
-2 + 5v2 + 3v4 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + 5v2 + 3v4 = 0

Factor a trinomial.
(-2 + -1v2)(1 + -3v2) = 0

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

Simplifying
-2 + -1v2 = 0

Solving
-2 + -1v2 = 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 + -1v2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1v2 = 0 + 2
-1v2 = 0 + 2

Combine like terms: 0 + 2 = 2
-1v2 = 2

Divide each side by '-1'.
v2 = -2

Simplifying
v2 = -2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(1 + -3v2)' equal to zero and attempt to solve:

Simplifying
1 + -3v2 = 0

Solving
1 + -3v2 = 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 + -3v2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3v2 = 0 + -1
-3v2 = 0 + -1

Combine like terms: 0 + -1 = -1
-3v2 = -1

Divide each side by '-3'.
v2 = 0.3333333333

Simplifying
v2 = 0.3333333333

Take the square root of each side:
v = {-0.577350269, 0.577350269}
Solution
v = {-0.577350269, 0.577350269}