(5m-4n)(2m+12n)=0

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Solution for (5m-4n)(2m+12n)=0 equation: 


Simplifying
(5m + -4n)(2m + 12n) = 0

Multiply (5m + -4n) * (2m + 12n)
(5m * (2m + 12n) + -4n * (2m + 12n)) = 0
((2m * 5m + 12n * 5m) + -4n * (2m + 12n)) = 0

Reorder the terms:
((60mn + 10m2) + -4n * (2m + 12n)) = 0
((60mn + 10m2) + -4n * (2m + 12n)) = 0
(60mn + 10m2 + (2m * -4n + 12n * -4n)) = 0
(60mn + 10m2 + (-8mn + -48n2)) = 0

Reorder the terms:
(60mn + -8mn + 10m2 + -48n2) = 0

Combine like terms: 60mn + -8mn = 52mn
(52mn + 10m2 + -48n2) = 0

Solving
52mn + 10m2 + -48n2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '2'.
2(26mn + 5m2 + -24n2) = 0

Factor a trinomial.
2((5m + -4n)(m + 6n)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(5m + -4n)' equal to zero and attempt to solve:

Simplifying
5m + -4n = 0

Solving
5m + -4n = 0

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

Add '4n' to each side of the equation.
5m + -4n + 4n = 0 + 4n

Combine like terms: -4n + 4n = 0
5m + 0 = 0 + 4n
5m = 0 + 4n
Remove the zero:
5m = 4n

Divide each side by '5'.
m = 0.8n

Simplifying
m = 0.8n

Subproblem 2
Set the factor '(m + 6n)' equal to zero and attempt to solve:

Simplifying
m + 6n = 0

Solving
m + 6n = 0

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

Add '-6n' to each side of the equation.
m + 6n + -6n = 0 + -6n

Combine like terms: 6n + -6n = 0
m + 0 = 0 + -6n
m = 0 + -6n
Remove the zero:
m = -6n

Simplifying
m = -6n
Solution
m = {0.8n, -6n}

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