-240x^4+144x^2-12=0

Solution for -240x^4+144x^2-12=0 equation:

Simplifying
-240x4 + 144x2 + -12 = 0

Reorder the terms:
-12 + 144x2 + -240x4 = 0

Solving
-12 + 144x2 + -240x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12'.
12(-1 + 12x2 + -20x4) = 0

Factor a trinomial.
12((-1 + 2x2)(1 + -10x2)) = 0

Ignore the factor 12.
Subproblem 1
Set the factor '(-1 + 2x2)' equal to zero and attempt to solve:

Simplifying
-1 + 2x2 = 0

Solving
-1 + 2x2 = 0

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

Add '1' to each side of the equation.
-1 + 1 + 2x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 2x2 = 0 + 1
2x2 = 0 + 1

Combine like terms: 0 + 1 = 1
2x2 = 1

Divide each side by '2'.
x2 = 0.5

Simplifying
x2 = 0.5

Take the square root of each side:
x = {-0.707106781, 0.707106781}
Subproblem 2
Set the factor '(1 + -10x2)' equal to zero and attempt to solve:

Simplifying
1 + -10x2 = 0

Solving
1 + -10x2 = 0

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

Add '-1' to each side of the equation.
1 + -1 + -10x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -10x2 = 0 + -1
-10x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-10x2 = -1

Divide each side by '-10'.
x2 = 0.1

Simplifying
x2 = 0.1

Take the square root of each side:
x = {-0.316227766, 0.316227766}
Solution
x = {-0.707106781, 0.707106781, -0.316227766, 0.316227766}