X(x+2)(3x-1)=0

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Solution for X(x+2)(3x-1)=0 equation: 


Simplifying
X(x + 2)(3x + -1) = 0

Reorder the terms:
X(2 + x)(3x + -1) = 0

Reorder the terms:
X(2 + x)(-1 + 3x) = 0

Multiply (2 + x) * (-1 + 3x)
X(2(-1 + 3x) + x(-1 + 3x)) = 0
X((-1 * 2 + 3x * 2) + x(-1 + 3x)) = 0
X((-2 + 6x) + x(-1 + 3x)) = 0
X(-2 + 6x + (-1 * x + 3x * x)) = 0
X(-2 + 6x + (-1x + 3x2)) = 0

Combine like terms: 6x + -1x = 5x
X(-2 + 5x + 3x2) = 0
(-2 * X + 5x * X + 3x2 * X) = 0
(-2X + 5xX + 3x2X) = 0

Solving
-2X + 5xX + 3x2X = 0

Solving for variable 'X'.

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

Factor out the Greatest Common Factor (GCF), 'X'.
X(-2 + 5x + 3x2) = 0

Factor a trinomial.
X((-2 + -1x)(1 + -3x)) = 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 '(-2 + -1x)' equal to zero and attempt to solve:

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 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 + -1x = 0 + 2

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

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

Add 'x' to each side of the equation.
-1x + x = 2 + x

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

Simplifying
0 = 2 + x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 3
Set the factor '(1 + -3x)' equal to zero and attempt to solve:

Simplifying
1 + -3x = 0

Solving
1 + -3x = 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 + -3x = 0 + -1

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

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

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

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

Simplifying
0 = -1 + 3x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
X = {0}

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