(5m-4n)(4m+6n)=

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Solution for (5m-4n)(4m+6n)= equation: 


Simplifying
(5m + -4n)(4m + 6n) = 0

Multiply (5m + -4n) * (4m + 6n)
(5m * (4m + 6n) + -4n * (4m + 6n)) = 0
((4m * 5m + 6n * 5m) + -4n * (4m + 6n)) = 0

Reorder the terms:
((30mn + 20m2) + -4n * (4m + 6n)) = 0
((30mn + 20m2) + -4n * (4m + 6n)) = 0
(30mn + 20m2 + (4m * -4n + 6n * -4n)) = 0
(30mn + 20m2 + (-16mn + -24n2)) = 0

Reorder the terms:
(30mn + -16mn + 20m2 + -24n2) = 0

Combine like terms: 30mn + -16mn = 14mn
(14mn + 20m2 + -24n2) = 0

Solving
14mn + 20m2 + -24n2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '2'.
2(7mn + 10m2 + -12n2) = 0

Factor a trinomial.
2((5m + -4n)(2m + 3n)) = 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 '(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 = {0.8n, -1.5n}

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