64x^4-x^2=0

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

Simplifying
64x4 + -1x2 = 0

Reorder the terms:
-1x2 + 64x4 = 0

Solving
-1x2 + 64x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(-1 + 64x2) = 0

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

Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}
Subproblem 2
Set the factor '(1 + 8x)' equal to zero and attempt to solve:

Simplifying
1 + 8x = 0

Solving
1 + 8x = 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 + 8x = 0 + -1

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

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

Divide each side by '8'.
x = -0.125

Simplifying
x = -0.125
Subproblem 3
Set the factor '(-1 + 8x)' equal to zero and attempt to solve:

Simplifying
-1 + 8x = 0

Solving
-1 + 8x = 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 + 8x = 0 + 1

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

Combine like terms: 0 + 1 = 1
8x = 1

Divide each side by '8'.
x = 0.125

Simplifying
x = 0.125
Solution
x = {0, -0.125, 0.125}