2x^4-64x^2+120=0

Solution for 2x^4-64x^2+120=0 equation:

Simplifying
2x4 + -64x2 + 120 = 0

Reorder the terms:
120 + -64x2 + 2x4 = 0

Solving
120 + -64x2 + 2x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(60 + -32x2 + x4) = 0

Factor a trinomial.
2((2 + -1x2)(30 + -1x2)) = 0

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

Simplifying
2 + -1x2 = 0

Solving
2 + -1x2 = 0

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

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

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

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

Divide each side by '-1'.
x2 = 2

Simplifying
x2 = 2

Take the square root of each side:
x = {-1.414213562, 1.414213562}
Subproblem 2
Set the factor '(30 + -1x2)' equal to zero and attempt to solve:

Simplifying
30 + -1x2 = 0

Solving
30 + -1x2 = 0

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

Add '-30' to each side of the equation.
30 + -30 + -1x2 = 0 + -30

Combine like terms: 30 + -30 = 0
0 + -1x2 = 0 + -30
-1x2 = 0 + -30

Combine like terms: 0 + -30 = -30
-1x2 = -30

Divide each side by '-1'.
x2 = 30

Simplifying
x2 = 30

Take the square root of each side:
x = {-5.477225575, 5.477225575}
Solution
x = {-1.414213562, 1.414213562, -5.477225575, 5.477225575}