2x^4-66x^2=-64

Solution for 2x^4-66x^2=-64 equation:

Simplifying
2x4 + -66x2 = -64

Reorder the terms:
-66x2 + 2x4 = -64

Solving
-66x2 + 2x4 = -64

Solving for variable 'x'.

Reorder the terms:
64 + -66x2 + 2x4 = -64 + 64

Combine like terms: -64 + 64 = 0
64 + -66x2 + 2x4 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(32 + -33x2 + x4) = 0

Factor a trinomial.
2((1 + -1x2)(32 + -1x2)) = 0

Factor a difference between two squares.
2(((1 + x)(1 + -1x))(32 + -1x2)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(32 + -1x2)' equal to zero and attempt to solve:

Simplifying
32 + -1x2 = 0

Solving
32 + -1x2 = 0

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

Add '-32' to each side of the equation.
32 + -32 + -1x2 = 0 + -32

Combine like terms: 32 + -32 = 0
0 + -1x2 = 0 + -32
-1x2 = 0 + -32

Combine like terms: 0 + -32 = -32
-1x2 = -32

Divide each side by '-1'.
x2 = 32

Simplifying
x2 = 32

Take the square root of each side:
x = {-5.656854249, 5.656854249}
Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 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 + x = 0 + -1

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

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

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 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 + -1x = 0 + -1

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

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

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

Simplifying
x = 1
Solution
x = {-5.656854249, 5.656854249, -1, 1}