100x^3=x

Solution for 100x^3=x equation:

Simplifying
100x3 = x

Solving
100x3 = x

Solving for variable 'x'.

Reorder the terms:
-1x + 100x3 = x + -1x

Combine like terms: x + -1x = 0
-1x + 100x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-1 + 100x2) = 0

Factor a difference between two squares.
x((1 + 10x)(-1 + 10x)) = 0

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

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(1 + 10x)' equal to zero and attempt to solve:

Simplifying
1 + 10x = 0

Solving
1 + 10x = 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 + 10x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 10x = 0 + -1
10x = 0 + -1

Combine like terms: 0 + -1 = -1
10x = -1

Divide each side by '10'.
x = -0.1

Simplifying
x = -0.1
Subproblem 3
Set the factor '(-1 + 10x)' equal to zero and attempt to solve:

Simplifying
-1 + 10x = 0

Solving
-1 + 10x = 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 + 10x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 10x = 0 + 1
10x = 0 + 1

Combine like terms: 0 + 1 = 1
10x = 1

Divide each side by '10'.
x = 0.1

Simplifying
x = 0.1
Solution
x = {0, -0.1, 0.1}