0=x^3-x^2-6x

Solution for 0=x^3-x^2-6x equation:

Simplifying
0 = x3 + -1x2 + -6x

Reorder the terms:
0 = -6x + -1x2 + x3

Solving
0 = -6x + -1x2 + x3

Solving for variable 'x'.
Remove the zero:
6x + x2 + -1x3 = -6x + -1x2 + x3 + 6x + x2 + -1x3

Reorder the terms:
6x + x2 + -1x3 = -6x + 6x + -1x2 + x2 + x3 + -1x3

Combine like terms: -6x + 6x = 0
6x + x2 + -1x3 = 0 + -1x2 + x2 + x3 + -1x3
6x + x2 + -1x3 = -1x2 + x2 + x3 + -1x3

Combine like terms: -1x2 + x2 = 0
6x + x2 + -1x3 = 0 + x3 + -1x3
6x + x2 + -1x3 = x3 + -1x3

Combine like terms: x3 + -1x3 = 0
6x + x2 + -1x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(6 + x + -1x2) = 0

Factor a trinomial.
x((3 + -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 '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
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, 3, -2}