v^4-v^2-6=0

Solution for v^4-v^2-6=0 equation:

Simplifying
v4 + -1v2 + -6 = 0

Reorder the terms:
-6 + -1v2 + v4 = 0

Solving
-6 + -1v2 + v4 = 0

Solving for variable 'v'.

Factor a trinomial.
(-2 + -1v2)(3 + -1v2) = 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 '(3 + -1v2)' equal to zero and attempt to solve:

Simplifying
3 + -1v2 = 0

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

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

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

Divide each side by '-1'.
v2 = 3

Simplifying
v2 = 3

Take the square root of each side:
v = {-1.732050808, 1.732050808}
Solution
v = {-1.732050808, 1.732050808}