2x^4-2x^2=144

Solution for 2x^4-2x^2=144 equation:

Simplifying
2x4 + -2x2 = 144

Reorder the terms:
-2x2 + 2x4 = 144

Solving
-2x2 + 2x4 = 144

Solving for variable 'x'.

Reorder the terms:
-144 + -2x2 + 2x4 = 144 + -144

Combine like terms: 144 + -144 = 0
-144 + -2x2 + 2x4 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-72 + -1x2 + x4) = 0

Factor a trinomial.
2((-8 + -1x2)(9 + -1x2)) = 0

Factor a difference between two squares.
2((-8 + -1x2)((3 + x)(3 + -1x))) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-8 + -1x2)' equal to zero and attempt to solve:

Simplifying
-8 + -1x2 = 0

Solving
-8 + -1x2 = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1x2 = 0 + 8
-1x2 = 0 + 8

Combine like terms: 0 + 8 = 8
-1x2 = 8

Divide each side by '-1'.
x2 = -8

Simplifying
x2 = -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 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

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

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

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

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

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

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

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

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

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

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