(x^5+x^3+x)(x^2-1)=0

Solution for (x^5+x^3+x)(x^2-1)=0 equation:

Simplifying
(x5 + x3 + x)(x2 + -1) = 0

Reorder the terms:
(x + x3 + x5)(x2 + -1) = 0

Reorder the terms:
(x + x3 + x5)(-1 + x2) = 0

Multiply (x + x3 + x5) * (-1 + x2)
(x(-1 + x2) + x3(-1 + x2) + x5(-1 + x2)) = 0
((-1 * x + x2 * x) + x3(-1 + x2) + x5(-1 + x2)) = 0
((-1x + x3) + x3(-1 + x2) + x5(-1 + x2)) = 0
(-1x + x3 + (-1 * x3 + x2 * x3) + x5(-1 + x2)) = 0
(-1x + x3 + (-1x3 + x5) + x5(-1 + x2)) = 0
(-1x + x3 + -1x3 + x5 + (-1 * x5 + x2 * x5)) = 0
(-1x + x3 + -1x3 + x5 + (-1x5 + x7)) = 0

Combine like terms: x3 + -1x3 = 0
(-1x + 0 + x5 + -1x5 + x7) = 0
(-1x + x5 + -1x5 + x7) = 0

Combine like terms: x5 + -1x5 = 0
(-1x + 0 + x7) = 0
(-1x + x7) = 0

Solving
-1x + x7 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-1 + x6) = 0

Factor a difference between two squares.
x((1 + x3)(-1 + x3)) = 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 + x3)' equal to zero and attempt to solve:

Simplifying
1 + x3 = 0

Solving
1 + x3 = 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 + x3 = 0 + -1

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

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

Simplifying
x3 = -1

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 + x3)' equal to zero and attempt to solve:

Simplifying
-1 + x3 = 0

Solving
-1 + x3 = 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 + x3 = 0 + 1

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

Combine like terms: 0 + 1 = 1
x3 = 1

Simplifying
x3 = 1

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}