64x^7-x^3=0

Solution for 64x^7-x^3=0 equation:

Simplifying
64x7 + -1x3 = 0

Reorder the terms:
-1x3 + 64x7 = 0

Solving
-1x3 + 64x7 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x3'.
x3(-1 + 64x4) = 0

Factor a difference between two squares.
x3((1 + 8x2)(-1 + 8x2)) = 0

Subproblem 1
Set the factor 'x3' equal to zero and attempt to solve:

Simplifying
x3 = 0

Solving
x3 = 0

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

Simplifying
x3 = 0

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 '(1 + 8x2)' equal to zero and attempt to solve:

Simplifying
1 + 8x2 = 0

Solving
1 + 8x2 = 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 + 8x2 = 0 + -1

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

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

Divide each side by '8'.
x2 = -0.125

Simplifying
x2 = -0.125

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 3
Set the factor '(-1 + 8x2)' equal to zero and attempt to solve:

Simplifying
-1 + 8x2 = 0

Solving
-1 + 8x2 = 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 + 8x2 = 0 + 1

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

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

Divide each side by '8'.
x2 = 0.125

Simplifying
x2 = 0.125

Take the square root of each side:
x = {-0.353553391, 0.353553391}
Solution
x = {-0.353553391, 0.353553391}