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

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


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

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

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

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

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

Solving
3X + -5xX + 2x2X = 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(3 + -5x + 2x2) = 0

Factor a trinomial.
X((1 + -1x)(3 + -2x)) = 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

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

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

Simplifying
0 = -1 + 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 '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 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 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Add '2x' to each side of the equation.
-2x + 2x = -3 + 2x

Combine like terms: -2x + 2x = 0
0 = -3 + 2x

Simplifying
0 = -3 + 2x

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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