ab(3a+6)4a(2a+b)2a(7a+3ab+4b)=

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Solution for ab(3a+6)4a(2a+b)2a(7a+3ab+4b)= equation: 


Simplifying
ab(3a + 6) * 4a(2a + b) * 2a(7a + 3ab + 4b) = 0

Reorder the terms:
ab(6 + 3a) * 4a(2a + b) * 2a(7a + 3ab + 4b) = 0

Reorder the terms for easier multiplication:
4 * 2ab * a * a(6 + 3a)(2a + b)(7a + 3ab + 4b) = 0

Multiply 4 * 2
8ab * a * a(6 + 3a)(2a + b)(7a + 3ab + 4b) = 0

Multiply ab * a
8a2b * a(6 + 3a)(2a + b)(7a + 3ab + 4b) = 0

Multiply a2b * a
8a3b(6 + 3a)(2a + b)(7a + 3ab + 4b) = 0

Multiply (6 + 3a) * (2a + b)
8a3b(6(2a + b) + 3a * (2a + b))(7a + 3ab + 4b) = 0
8a3b((2a * 6 + b * 6) + 3a * (2a + b))(7a + 3ab + 4b) = 0
8a3b((12a + 6b) + 3a * (2a + b))(7a + 3ab + 4b) = 0
8a3b(12a + 6b + (2a * 3a + b * 3a))(7a + 3ab + 4b) = 0

Reorder the terms:
8a3b(12a + 6b + (3ab + 6a2))(7a + 3ab + 4b) = 0
8a3b(12a + 6b + (3ab + 6a2))(7a + 3ab + 4b) = 0

Reorder the terms:
8a3b(12a + 3ab + 6a2 + 6b)(7a + 3ab + 4b) = 0
8a3b(12a + 3ab + 6a2 + 6b)(7a + 3ab + 4b) = 0

Multiply (12a + 3ab + 6a2 + 6b) * (7a + 3ab + 4b)
8a3b(12a * (7a + 3ab + 4b) + 3ab * (7a + 3ab + 4b) + 6a2 * (7a + 3ab + 4b) + 6b * (7a + 3ab + 4b)) = 0
8a3b((7a * 12a + 3ab * 12a + 4b * 12a) + 3ab * (7a + 3ab + 4b) + 6a2 * (7a + 3ab + 4b) + 6b * (7a + 3ab + 4b)) = 0

Reorder the terms:
8a3b((48ab + 84a2 + 36a2b) + 3ab * (7a + 3ab + 4b) + 6a2 * (7a + 3ab + 4b) + 6b * (7a + 3ab + 4b)) = 0
8a3b((48ab + 84a2 + 36a2b) + 3ab * (7a + 3ab + 4b) + 6a2 * (7a + 3ab + 4b) + 6b * (7a + 3ab + 4b)) = 0
8a3b(48ab + 84a2 + 36a2b + (7a * 3ab + 3ab * 3ab + 4b * 3ab) + 6a2 * (7a + 3ab + 4b) + 6b * (7a + 3ab + 4b)) = 0

Reorder the terms:
8a3b(48ab + 84a2 + 36a2b + (12ab2 + 21a2b + 9a2b2) + 6a2 * (7a + 3ab + 4b) + 6b * (7a + 3ab + 4b)) = 0
8a3b(48ab + 84a2 + 36a2b + (12ab2 + 21a2b + 9a2b2) + 6a2 * (7a + 3ab + 4b) + 6b * (7a + 3ab + 4b)) = 0
8a3b(48ab + 84a2 + 36a2b + 12ab2 + 21a2b + 9a2b2 + (7a * 6a2 + 3ab * 6a2 + 4b * 6a2) + 6b * (7a + 3ab + 4b)) = 0

Reorder the terms:
8a3b(48ab + 84a2 + 36a2b + 12ab2 + 21a2b + 9a2b2 + (24a2b + 42a3 + 18a3b) + 6b * (7a + 3ab + 4b)) = 0
8a3b(48ab + 84a2 + 36a2b + 12ab2 + 21a2b + 9a2b2 + (24a2b + 42a3 + 18a3b) + 6b * (7a + 3ab + 4b)) = 0
8a3b(48ab + 84a2 + 36a2b + 12ab2 + 21a2b + 9a2b2 + 24a2b + 42a3 + 18a3b + (7a * 6b + 3ab * 6b + 4b * 6b)) = 0
8a3b(48ab + 84a2 + 36a2b + 12ab2 + 21a2b + 9a2b2 + 24a2b + 42a3 + 18a3b + (42ab + 18ab2 + 24b2)) = 0

Reorder the terms:
8a3b(48ab + 42ab + 12ab2 + 18ab2 + 84a2 + 36a2b + 21a2b + 24a2b + 9a2b2 + 42a3 + 18a3b + 24b2) = 0

Combine like terms: 48ab + 42ab = 90ab
8a3b(90ab + 12ab2 + 18ab2 + 84a2 + 36a2b + 21a2b + 24a2b + 9a2b2 + 42a3 + 18a3b + 24b2) = 0

Combine like terms: 12ab2 + 18ab2 = 30ab2
8a3b(90ab + 30ab2 + 84a2 + 36a2b + 21a2b + 24a2b + 9a2b2 + 42a3 + 18a3b + 24b2) = 0

Combine like terms: 36a2b + 21a2b = 57a2b
8a3b(90ab + 30ab2 + 84a2 + 57a2b + 24a2b + 9a2b2 + 42a3 + 18a3b + 24b2) = 0

Combine like terms: 57a2b + 24a2b = 81a2b
8a3b(90ab + 30ab2 + 84a2 + 81a2b + 9a2b2 + 42a3 + 18a3b + 24b2) = 0
(90ab * 8a3b + 30ab2 * 8a3b + 84a2 * 8a3b + 81a2b * 8a3b + 9a2b2 * 8a3b + 42a3 * 8a3b + 18a3b * 8a3b + 24b2 * 8a3b) = 0

Reorder the terms:
(192a3b3 + 720a4b2 + 240a4b3 + 672a5b + 648a5b2 + 72a5b3 + 336a6b + 144a6b2) = 0
(192a3b3 + 720a4b2 + 240a4b3 + 672a5b + 648a5b2 + 72a5b3 + 336a6b + 144a6b2) = 0

Solving
192a3b3 + 720a4b2 + 240a4b3 + 672a5b + 648a5b2 + 72a5b3 + 336a6b + 144a6b2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '24a3b'.
24a3b(8b2 + 30ab + 10ab2 + 28a2 + 27a2b + 3a2b2 + 14a3 + 6a3b) = 0

Ignore the factor 24.

Subproblem 1
Set the factor 'a3b' equal to zero and attempt to solve:

Simplifying
a3b = 0

Solving
a3b = 0

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

Simplifying
a3b = 0

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 '(8b2 + 30ab + 10ab2 + 28a2 + 27a2b + 3a2b2 + 14a3 + 6a3b)' equal to zero and attempt to solve:

Simplifying
8b2 + 30ab + 10ab2 + 28a2 + 27a2b + 3a2b2 + 14a3 + 6a3b = 0

Reorder the terms:
30ab + 10ab2 + 28a2 + 27a2b + 3a2b2 + 14a3 + 6a3b + 8b2 = 0

Solving
30ab + 10ab2 + 28a2 + 27a2b + 3a2b2 + 14a3 + 6a3b + 8b2 = 0

The solution to this equation could not be determined.

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

The solution to this equation could not be determined.

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