w^4+5w^2-36=0

Solution for w^4+5w^2-36=0 equation:

Simplifying
w4 + 5w2 + -36 = 0

Reorder the terms:
-36 + 5w2 + w4 = 0

Solving
-36 + 5w2 + w4 = 0

Solving for variable 'w'.

Factor a trinomial.
(-9 + -1w2)(4 + -1w2) = 0

Factor a difference between two squares.
(-9 + -1w2)((2 + w)(2 + -1w)) = 0

Subproblem 1
Set the factor '(-9 + -1w2)' equal to zero and attempt to solve:

Simplifying
-9 + -1w2 = 0

Solving
-9 + -1w2 = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1w2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1w2 = 0 + 9
-1w2 = 0 + 9

Combine like terms: 0 + 9 = 9
-1w2 = 9

Divide each side by '-1'.
w2 = -9

Simplifying
w2 = -9

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

Simplifying
2 + w = 0

Solving
2 + w = 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 + w = 0 + -2

Combine like terms: 2 + -2 = 0
0 + w = 0 + -2
w = 0 + -2

Combine like terms: 0 + -2 = -2
w = -2

Simplifying
w = -2
Subproblem 3
Set the factor '(2 + -1w)' equal to zero and attempt to solve:

Simplifying
2 + -1w = 0

Solving
2 + -1w = 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 + -1w = 0 + -2

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

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

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

Simplifying
w = 2
Solution
w = {-2, 2}