w^4+9w^2-400=0

Solution for w^4+9w^2-400=0 equation:

Simplifying
w4 + 9w2 + -400 = 0

Reorder the terms:
-400 + 9w2 + w4 = 0

Solving
-400 + 9w2 + w4 = 0

Solving for variable 'w'.

Factor a trinomial.
(-25 + -1w2)(16 + -1w2) = 0

Factor a difference between two squares.
(-25 + -1w2)((4 + w)(4 + -1w)) = 0

Subproblem 1
Set the factor '(-25 + -1w2)' equal to zero and attempt to solve:

Simplifying
-25 + -1w2 = 0

Solving
-25 + -1w2 = 0

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

Add '25' to each side of the equation.
-25 + 25 + -1w2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -1w2 = 0 + 25
-1w2 = 0 + 25

Combine like terms: 0 + 25 = 25
-1w2 = 25

Divide each side by '-1'.
w2 = -25

Simplifying
w2 = -25

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 '(4 + w)' equal to zero and attempt to solve:

Simplifying
4 + w = 0

Solving
4 + w = 0

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

Add '-4' to each side of the equation.
4 + -4 + w = 0 + -4

Combine like terms: 4 + -4 = 0
0 + w = 0 + -4
w = 0 + -4

Combine like terms: 0 + -4 = -4
w = -4

Simplifying
w = -4
Subproblem 3
Set the factor '(4 + -1w)' equal to zero and attempt to solve:

Simplifying
4 + -1w = 0

Solving
4 + -1w = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1w = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1w = 0 + -4
-1w = 0 + -4

Combine like terms: 0 + -4 = -4
-1w = -4

Divide each side by '-1'.
w = 4

Simplifying
w = 4
Solution
w = {-4, 4}