(6m-4n)(2m+7n)=

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Solution for (6m-4n)(2m+7n)= equation: 


Simplifying
(6m + -4n)(2m + 7n) = 0

Multiply (6m + -4n) * (2m + 7n)
(6m * (2m + 7n) + -4n * (2m + 7n)) = 0
((2m * 6m + 7n * 6m) + -4n * (2m + 7n)) = 0

Reorder the terms:
((42mn + 12m2) + -4n * (2m + 7n)) = 0
((42mn + 12m2) + -4n * (2m + 7n)) = 0
(42mn + 12m2 + (2m * -4n + 7n * -4n)) = 0
(42mn + 12m2 + (-8mn + -28n2)) = 0

Reorder the terms:
(42mn + -8mn + 12m2 + -28n2) = 0

Combine like terms: 42mn + -8mn = 34mn
(34mn + 12m2 + -28n2) = 0

Solving
34mn + 12m2 + -28n2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '2'.
2(17mn + 6m2 + -14n2) = 0

Factor a trinomial.
2((3m + -2n)(2m + 7n)) = 0

Ignore the factor 2.

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

Simplifying
3m + -2n = 0

Solving
3m + -2n = 0

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

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

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

Divide each side by '3'.
m = 0.6666666667n

Simplifying
m = 0.6666666667n

Subproblem 2
Set the factor '(2m + 7n)' equal to zero and attempt to solve:

Simplifying
2m + 7n = 0

Solving
2m + 7n = 0

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

Add '-7n' to each side of the equation.
2m + 7n + -7n = 0 + -7n

Combine like terms: 7n + -7n = 0
2m + 0 = 0 + -7n
2m = 0 + -7n
Remove the zero:
2m = -7n

Divide each side by '2'.
m = -3.5n

Simplifying
m = -3.5n
Solution
m = {0.6666666667n, -3.5n}

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