X(2x-3)(4x-1)=0

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Solution for X(2x-3)(4x-1)=0 equation: 


Simplifying
X(2x + -3)(4x + -1) = 0

Reorder the terms:
X(-3 + 2x)(4x + -1) = 0

Reorder the terms:
X(-3 + 2x)(-1 + 4x) = 0

Multiply (-3 + 2x) * (-1 + 4x)
X(-3(-1 + 4x) + 2x * (-1 + 4x)) = 0
X((-1 * -3 + 4x * -3) + 2x * (-1 + 4x)) = 0
X((3 + -12x) + 2x * (-1 + 4x)) = 0
X(3 + -12x + (-1 * 2x + 4x * 2x)) = 0
X(3 + -12x + (-2x + 8x2)) = 0

Combine like terms: -12x + -2x = -14x
X(3 + -14x + 8x2) = 0
(3 * X + -14x * X + 8x2 * X) = 0
(3X + -14xX + 8x2X) = 0

Solving
3X + -14xX + 8x2X = 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 + -14x + 8x2) = 0

Factor a trinomial.
X((1 + -4x)(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 + -4x)' equal to zero and attempt to solve:

Simplifying
1 + -4x = 0

Solving
1 + -4x = 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 + -4x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4x = 0 + -1
-4x = 0 + -1

Combine like terms: 0 + -1 = -1
-4x = -1

Add '4x' to each side of the equation.
-4x + 4x = -1 + 4x

Combine like terms: -4x + 4x = 0
0 = -1 + 4x

Simplifying
0 = -1 + 4x

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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