0=x^3+2x^2+x

Solution for 0=x^3+2x^2+x equation:

Simplifying
0 = x3 + 2x2 + x

Reorder the terms:
0 = x + 2x2 + x3

Solving
0 = x + 2x2 + x3

Solving for variable 'x'.
Remove the zero:
-1x + -2x2 + -1x3 = x + 2x2 + x3 + -1x + -2x2 + -1x3

Reorder the terms:
-1x + -2x2 + -1x3 = x + -1x + 2x2 + -2x2 + x3 + -1x3

Combine like terms: x + -1x = 0
-1x + -2x2 + -1x3 = 0 + 2x2 + -2x2 + x3 + -1x3
-1x + -2x2 + -1x3 = 2x2 + -2x2 + x3 + -1x3

Combine like terms: 2x2 + -2x2 = 0
-1x + -2x2 + -1x3 = 0 + x3 + -1x3
-1x + -2x2 + -1x3 = x3 + -1x3

Combine like terms: x3 + -1x3 = 0
-1x + -2x2 + -1x3 = 0

Factor out the Greatest Common Factor (GCF), '-1x'.
-1x(1 + 2x + x2) = 0

Factor a trinomial.
-1x((1 + x)(1 + x)) = 0

Ignore the factor -1.
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}