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

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


Simplifying
0 = x3 + x2 + -2x

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

Solving
0 = -2x + x2 + x3

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

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

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

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

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

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

Factor a trinomial.
x((1 + -1x)(2 + 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 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

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

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

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

Divide each side by '-1'.
x = 1

Simplifying
x = 1

Subproblem 3
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Solution
x = {0, 1, -2}

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