625x^6-x^2=0

Solution for 625x^6-x^2=0 equation:

Simplifying
625x6 + -1x2 = 0

Reorder the terms:
-1x2 + 625x6 = 0

Solving
-1x2 + 625x6 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(-1 + 625x4) = 0

Factor a difference between two squares.
x2((1 + 25x2)(-1 + 25x2)) = 0

Factor a difference between two squares.
x2((1 + 25x2)((1 + 5x)(-1 + 5x))) = 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 + 25x2)' equal to zero and attempt to solve:

Simplifying
1 + 25x2 = 0

Solving
1 + 25x2 = 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 + 25x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 25x2 = 0 + -1
25x2 = 0 + -1

Combine like terms: 0 + -1 = -1
25x2 = -1

Divide each side by '25'.
x2 = -0.04

Simplifying
x2 = -0.04

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 + 5x)' equal to zero and attempt to solve:

Simplifying
1 + 5x = 0

Solving
1 + 5x = 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 + 5x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 5x = 0 + -1
5x = 0 + -1

Combine like terms: 0 + -1 = -1
5x = -1

Divide each side by '5'.
x = -0.2

Simplifying
x = -0.2
Subproblem 4
Set the factor '(-1 + 5x)' equal to zero and attempt to solve:

Simplifying
-1 + 5x = 0

Solving
-1 + 5x = 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 + 5x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 5x = 0 + 1
5x = 0 + 1

Combine like terms: 0 + 1 = 1
5x = 1

Divide each side by '5'.
x = 0.2

Simplifying
x = 0.2
Solution
x = {0, -0.2, 0.2}