2u^4-2u^2-144=0

Solution for 2u^4-2u^2-144=0 equation:

Simplifying
2u4 + -2u2 + -144 = 0

Reorder the terms:
-144 + -2u2 + 2u4 = 0

Solving
-144 + -2u2 + 2u4 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-72 + -1u2 + u4) = 0

Factor a trinomial.
2((-8 + -1u2)(9 + -1u2)) = 0

Factor a difference between two squares.
2((-8 + -1u2)((3 + u)(3 + -1u))) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-8 + -1u2)' equal to zero and attempt to solve:

Simplifying
-8 + -1u2 = 0

Solving
-8 + -1u2 = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1u2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1u2 = 0 + 8
-1u2 = 0 + 8

Combine like terms: 0 + 8 = 8
-1u2 = 8

Divide each side by '-1'.
u2 = -8

Simplifying
u2 = -8

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

Simplifying
3 + u = 0

Solving
3 + u = 0

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

Add '-3' to each side of the equation.
3 + -3 + u = 0 + -3

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

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

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

Simplifying
3 + -1u = 0

Solving
3 + -1u = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1u = 0 + -3

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

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

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

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