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

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

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

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

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

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

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

Solving
-1x + x3 = 0

Solving for variable 'x'.

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

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