a(2x+5)(3x-1)=0

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


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

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

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

Multiply (5 + 2x) * (-1 + 3x)
a(5(-1 + 3x) + 2x * (-1 + 3x)) = 0
a((-1 * 5 + 3x * 5) + 2x * (-1 + 3x)) = 0
a((-5 + 15x) + 2x * (-1 + 3x)) = 0
a(-5 + 15x + (-1 * 2x + 3x * 2x)) = 0
a(-5 + 15x + (-2x + 6x2)) = 0

Combine like terms: 15x + -2x = 13x
a(-5 + 13x + 6x2) = 0
(-5 * a + 13x * a + 6x2 * a) = 0
(-5a + 13ax + 6ax2) = 0

Solving
-5a + 13ax + 6ax2 = 0

Solving for variable 'a'.

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

Factor out the Greatest Common Factor (GCF), 'a'.
a(-5 + 13x + 6x2) = 0

Factor a trinomial.
a((-5 + -2x)(1 + -3x)) = 0


Subproblem 1
Set the factor 'a' equal to zero and attempt to solve:

Simplifying
a = 0

Solving
a = 0

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

Simplifying
a = 0

Subproblem 2
Set the factor '(-5 + -2x)' equal to zero and attempt to solve:

Simplifying
-5 + -2x = 0

Solving
-5 + -2x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -2x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2x = 0 + 5
-2x = 0 + 5

Combine like terms: 0 + 5 = 5
-2x = 5

Add '2x' to each side of the equation.
-2x + 2x = 5 + 2x

Combine like terms: -2x + 2x = 0
0 = 5 + 2x

Simplifying
0 = 5 + 2x

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 a 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
a = {0}

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