w^4+8w^2-9=0

Solution for w^4+8w^2-9=0 equation:

Simplifying
w4 + 8w2 + -9 = 0

Reorder the terms:
-9 + 8w2 + w4 = 0

Solving
-9 + 8w2 + w4 = 0

Solving for variable 'w'.

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

Factor a difference between two squares.
(-9 + -1w2)((1 + w)(1 + -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 '(1 + w)' equal to zero and attempt to solve:

Simplifying
1 + w = 0

Solving
1 + w = 0

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

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

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

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

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

Simplifying
1 + -1w = 0

Solving
1 + -1w = 0

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

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

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

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

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

Simplifying
w = 1
Solution
w = {-1, 1}