(4m+2n+6)(6m+4n+2)=0

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Solution for (4m+2n+6)(6m+4n+2)=0 equation: 


Simplifying
(4m + 2n + 6)(6m + 4n + 2) = 0

Reorder the terms:
(6 + 4m + 2n)(6m + 4n + 2) = 0

Reorder the terms:
(6 + 4m + 2n)(2 + 6m + 4n) = 0

Multiply (6 + 4m + 2n) * (2 + 6m + 4n)
(6(2 + 6m + 4n) + 4m * (2 + 6m + 4n) + 2n * (2 + 6m + 4n)) = 0
((2 * 6 + 6m * 6 + 4n * 6) + 4m * (2 + 6m + 4n) + 2n * (2 + 6m + 4n)) = 0
((12 + 36m + 24n) + 4m * (2 + 6m + 4n) + 2n * (2 + 6m + 4n)) = 0
(12 + 36m + 24n + (2 * 4m + 6m * 4m + 4n * 4m) + 2n * (2 + 6m + 4n)) = 0

Reorder the terms:
(12 + 36m + 24n + (8m + 16mn + 24m2) + 2n * (2 + 6m + 4n)) = 0
(12 + 36m + 24n + (8m + 16mn + 24m2) + 2n * (2 + 6m + 4n)) = 0
(12 + 36m + 24n + 8m + 16mn + 24m2 + (2 * 2n + 6m * 2n + 4n * 2n)) = 0

Reorder the terms:
(12 + 36m + 24n + 8m + 16mn + 24m2 + (12mn + 4n + 8n2)) = 0
(12 + 36m + 24n + 8m + 16mn + 24m2 + (12mn + 4n + 8n2)) = 0

Reorder the terms:
(12 + 36m + 8m + 16mn + 12mn + 24m2 + 24n + 4n + 8n2) = 0

Combine like terms: 36m + 8m = 44m
(12 + 44m + 16mn + 12mn + 24m2 + 24n + 4n + 8n2) = 0

Combine like terms: 16mn + 12mn = 28mn
(12 + 44m + 28mn + 24m2 + 24n + 4n + 8n2) = 0

Combine like terms: 24n + 4n = 28n
(12 + 44m + 28mn + 24m2 + 28n + 8n2) = 0

Solving
12 + 44m + 28mn + 24m2 + 28n + 8n2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '4'.
4(3 + 11m + 7mn + 6m2 + 7n + 2n2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(3 + 11m + 7mn + 6m2 + 7n + 2n2)' equal to zero and attempt to solve:

Simplifying
3 + 11m + 7mn + 6m2 + 7n + 2n2 = 0

Solving
3 + 11m + 7mn + 6m2 + 7n + 2n2 = 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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