0=X^3-2X^2-3X

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Solution for 0=X^3-2X^2-3X equation: 


Simplifying
0 = X3 + -2X2 + -3X

Reorder the terms:
0 = -3X + -2X2 + X3

Solving
0 = -3X + -2X2 + X3

Solving for variable 'X'.
Remove the zero:
3X + 2X2 + -1X3 = -3X + -2X2 + X3 + 3X + 2X2 + -1X3

Reorder the terms:
3X + 2X2 + -1X3 = -3X + 3X + -2X2 + 2X2 + X3 + -1X3

Combine like terms: -3X + 3X = 0
3X + 2X2 + -1X3 = 0 + -2X2 + 2X2 + X3 + -1X3
3X + 2X2 + -1X3 = -2X2 + 2X2 + X3 + -1X3

Combine like terms: -2X2 + 2X2 = 0
3X + 2X2 + -1X3 = 0 + X3 + -1X3
3X + 2X2 + -1X3 = X3 + -1X3

Combine like terms: X3 + -1X3 = 0
3X + 2X2 + -1X3 = 0

Factor out the Greatest Common Factor (GCF), 'X'.
X(3 + 2X + -1X2) = 0

Factor a trinomial.
X((3 + -1X)(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 '(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 '(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, 3, -1}

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