w^4+w^2-6=0

Solution for w^4+w^2-6=0 equation:

Simplifying
w4 + w2 + -6 = 0

Reorder the terms:
-6 + w2 + w4 = 0

Solving
-6 + w2 + w4 = 0

Solving for variable 'w'.

Factor a trinomial.
(-3 + -1w2)(2 + -1w2) = 0

Subproblem 1
Set the factor '(-3 + -1w2)' equal to zero and attempt to solve:

Simplifying
-3 + -1w2 = 0

Solving
-3 + -1w2 = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1w2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1w2 = 0 + 3
-1w2 = 0 + 3

Combine like terms: 0 + 3 = 3
-1w2 = 3

Divide each side by '-1'.
w2 = -3

Simplifying
w2 = -3

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 '(2 + -1w2)' equal to zero and attempt to solve:

Simplifying
2 + -1w2 = 0

Solving
2 + -1w2 = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1w2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1w2 = 0 + -2
-1w2 = 0 + -2

Combine like terms: 0 + -2 = -2
-1w2 = -2

Divide each side by '-1'.
w2 = 2

Simplifying
w2 = 2

Take the square root of each side:
w = {-1.414213562, 1.414213562}
Solution
w = {-1.414213562, 1.414213562}