(2m+3n)(4m+6n)=0

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Solution for (2m+3n)(4m+6n)=0 equation: 


Simplifying
(2m + 3n)(4m + 6n) = 0

Multiply (2m + 3n) * (4m + 6n)
(2m * (4m + 6n) + 3n * (4m + 6n)) = 0
((4m * 2m + 6n * 2m) + 3n * (4m + 6n)) = 0

Reorder the terms:
((12mn + 8m2) + 3n * (4m + 6n)) = 0
((12mn + 8m2) + 3n * (4m + 6n)) = 0
(12mn + 8m2 + (4m * 3n + 6n * 3n)) = 0
(12mn + 8m2 + (12mn + 18n2)) = 0

Reorder the terms:
(12mn + 12mn + 8m2 + 18n2) = 0

Combine like terms: 12mn + 12mn = 24mn
(24mn + 8m2 + 18n2) = 0

Solving
24mn + 8m2 + 18n2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '2'.
2(12mn + 4m2 + 9n2) = 0

Factor a trinomial.
2((2m + 3n)(2m + 3n)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(2m + 3n)' equal to zero and attempt to solve:

Simplifying
2m + 3n = 0

Solving
2m + 3n = 0

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

Add '-3n' to each side of the equation.
2m + 3n + -3n = 0 + -3n

Combine like terms: 3n + -3n = 0
2m + 0 = 0 + -3n
2m = 0 + -3n
Remove the zero:
2m = -3n

Divide each side by '2'.
m = -1.5n

Simplifying
m = -1.5n

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

Simplifying
2m + 3n = 0

Solving
2m + 3n = 0

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

Add '-3n' to each side of the equation.
2m + 3n + -3n = 0 + -3n

Combine like terms: 3n + -3n = 0
2m + 0 = 0 + -3n
2m = 0 + -3n
Remove the zero:
2m = -3n

Divide each side by '2'.
m = -1.5n

Simplifying
m = -1.5n
Solution
m = {-1.5n, -1.5n}

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