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

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


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

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