(a+b)(2a+3b)(2xy)=0

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Solution for (a+b)(2a+3b)(2xy)=0 equation: 


Simplifying
(a + b)(2a + 3b)(2xy) = 0

Remove parenthesis around (2xy)
(a + b)(2a + 3b) * 2xy = 0

Reorder the terms for easier multiplication:
2xy(a + b)(2a + 3b) = 0

Multiply (a + b) * (2a + 3b)
2xy(a(2a + 3b) + b(2a + 3b)) = 0
2xy((2a * a + 3b * a) + b(2a + 3b)) = 0

Reorder the terms:
2xy((3ab + 2a2) + b(2a + 3b)) = 0
2xy((3ab + 2a2) + b(2a + 3b)) = 0
2xy(3ab + 2a2 + (2a * b + 3b * b)) = 0
2xy(3ab + 2a2 + (2ab + 3b2)) = 0

Reorder the terms:
2xy(3ab + 2ab + 2a2 + 3b2) = 0

Combine like terms: 3ab + 2ab = 5ab
2xy(5ab + 2a2 + 3b2) = 0
(5ab * 2xy + 2a2 * 2xy + 3b2 * 2xy) = 0
(10abxy + 4a2xy + 6b2xy) = 0

Solving
10abxy + 4a2xy + 6b2xy = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2xy'.
2xy(5ab + 2a2 + 3b2) = 0

Factor a trinomial.
2xy((a + b)(2a + 3b)) = 0

Ignore the factor 2.

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

Simplifying
xy = 0

Solving
xy = 0

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

Add '-1xy' to each side of the equation.
xy + -1xy = 0 + -1xy
Remove the zero:
0 = -1xy

Simplifying
0 = -1xy

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(a + b)' equal to zero and attempt to solve:

Simplifying
a + b = 0

Solving
a + b = 0

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

Add '-1b' to each side of the equation.
a + b + -1b = 0 + -1b

Combine like terms: b + -1b = 0
a + 0 = 0 + -1b
a = 0 + -1b
Remove the zero:
a = -1b

Simplifying
a = -1b

Subproblem 3
Set the factor '(2a + 3b)' equal to zero and attempt to solve:

Simplifying
2a + 3b = 0

Solving
2a + 3b = 0

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

Add '-3b' to each side of the equation.
2a + 3b + -3b = 0 + -3b

Combine like terms: 3b + -3b = 0
2a + 0 = 0 + -3b
2a = 0 + -3b
Remove the zero:
2a = -3b

Divide each side by '2'.
a = -1.5b

Simplifying
a = -1.5b
Solution
a = {-1b, -1.5b}

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