(x^2+x)(x^2-x)=0

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

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

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

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

Multiply (x + x2) * (-1x + x2)
(x(-1x + x2) + x2(-1x + x2)) = 0
((-1x * x + x2 * x) + x2(-1x + x2)) = 0
((-1x2 + x3) + x2(-1x + x2)) = 0
(-1x2 + x3 + (-1x * x2 + x2 * x2)) = 0
(-1x2 + x3 + (-1x3 + x4)) = 0

Combine like terms: x3 + -1x3 = 0
(-1x2 + 0 + x4) = 0
(-1x2 + x4) = 0

Solving
-1x2 + x4 = 0

Solving for variable 'x'.

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

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

Simplifying
1 + x = 0

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

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

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

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

Simplifying
-1 + x = 0

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

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

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

Simplifying
x = 1
Solution
x = {0, -1, 1}