w^4+7w^2-144=0

Solution for w^4+7w^2-144=0 equation:

Simplifying
w4 + 7w2 + -144 = 0

Reorder the terms:
-144 + 7w2 + w4 = 0

Solving
-144 + 7w2 + w4 = 0

Solving for variable 'w'.

Factor a trinomial.
(-16 + -1w2)(9 + -1w2) = 0

Factor a difference between two squares.
(-16 + -1w2)((3 + w)(3 + -1w)) = 0

Subproblem 1
Set the factor '(-16 + -1w2)' equal to zero and attempt to solve:

Simplifying
-16 + -1w2 = 0

Solving
-16 + -1w2 = 0

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

Add '16' to each side of the equation.
-16 + 16 + -1w2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -1w2 = 0 + 16
-1w2 = 0 + 16

Combine like terms: 0 + 16 = 16
-1w2 = 16

Divide each side by '-1'.
w2 = -16

Simplifying
w2 = -16

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

Simplifying
3 + w = 0

Solving
3 + w = 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 + w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + w = 0 + -3
w = 0 + -3

Combine like terms: 0 + -3 = -3
w = -3

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

Simplifying
3 + -1w = 0

Solving
3 + -1w = 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 + -1w = 0 + -3

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

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

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

Simplifying
w = 3
Solution
w = {-3, 3}