X(2x-1)(5-3x)=0

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Solution for X(2x-1)(5-3x)=0 equation: 


Simplifying
X(2x + -1)(5 + -3x) = 0

Reorder the terms:
X(-1 + 2x)(5 + -3x) = 0

Multiply (-1 + 2x) * (5 + -3x)
X(-1(5 + -3x) + 2x * (5 + -3x)) = 0
X((5 * -1 + -3x * -1) + 2x * (5 + -3x)) = 0
X((-5 + 3x) + 2x * (5 + -3x)) = 0
X(-5 + 3x + (5 * 2x + -3x * 2x)) = 0
X(-5 + 3x + (10x + -6x2)) = 0

Combine like terms: 3x + 10x = 13x
X(-5 + 13x + -6x2) = 0
(-5 * X + 13x * X + -6x2 * X) = 0
(-5X + 13xX + -6x2X) = 0

Solving
-5X + 13xX + -6x2X = 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(-5 + 13x + -6x2) = 0

Factor a trinomial.
X((-5 + 3x)(1 + -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 '(-5 + 3x)' equal to zero and attempt to solve:

Simplifying
-5 + 3x = 0

Solving
-5 + 3x = 0

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

Add '5' to each side of the equation.
-5 + 5 + 3x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 3x = 0 + 5
3x = 0 + 5

Combine like terms: 0 + 5 = 5
3x = 5

Add '-3x' to each side of the equation.
3x + -3x = 5 + -3x

Combine like terms: 3x + -3x = 0
0 = 5 + -3x

Simplifying
0 = 5 + -3x

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 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

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

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

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

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

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

Simplifying
0 = -1 + 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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