w^4+w^2=30

Solution for w^4+w^2=30 equation:

Simplifying
w4 + w2 = 30

Reorder the terms:
w2 + w4 = 30

Solving
w2 + w4 = 30

Solving for variable 'w'.

Reorder the terms:
-30 + w2 + w4 = 30 + -30

Combine like terms: 30 + -30 = 0
-30 + w2 + w4 = 0

Factor a trinomial.
(-6 + -1w2)(5 + -1w2) = 0

Subproblem 1
Set the factor '(-6 + -1w2)' equal to zero and attempt to solve:

Simplifying
-6 + -1w2 = 0

Solving
-6 + -1w2 = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1w2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1w2 = 0 + 6
-1w2 = 0 + 6

Combine like terms: 0 + 6 = 6
-1w2 = 6

Divide each side by '-1'.
w2 = -6

Simplifying
w2 = -6

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 '(5 + -1w2)' equal to zero and attempt to solve:

Simplifying
5 + -1w2 = 0

Solving
5 + -1w2 = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1w2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1w2 = 0 + -5
-1w2 = 0 + -5

Combine like terms: 0 + -5 = -5
-1w2 = -5

Divide each side by '-1'.
w2 = 5

Simplifying
w2 = 5

Take the square root of each side:
w = {-2.236067978, 2.236067978}
Solution
w = {-2.236067978, 2.236067978}