(5m-3n)(4m-2n)=0

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Solution for (5m-3n)(4m-2n)=0 equation: 


Simplifying
(5m + -3n)(4m + -2n) = 0

Multiply (5m + -3n) * (4m + -2n)
(5m * (4m + -2n) + -3n * (4m + -2n)) = 0
((4m * 5m + -2n * 5m) + -3n * (4m + -2n)) = 0

Reorder the terms:
((-10mn + 20m2) + -3n * (4m + -2n)) = 0
((-10mn + 20m2) + -3n * (4m + -2n)) = 0
(-10mn + 20m2 + (4m * -3n + -2n * -3n)) = 0
(-10mn + 20m2 + (-12mn + 6n2)) = 0

Reorder the terms:
(-10mn + -12mn + 20m2 + 6n2) = 0

Combine like terms: -10mn + -12mn = -22mn
(-22mn + 20m2 + 6n2) = 0

Solving
-22mn + 20m2 + 6n2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-11mn + 10m2 + 3n2) = 0

Factor a trinomial.
2((5m + -3n)(2m + -1n)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(5m + -3n)' equal to zero and attempt to solve:

Simplifying
5m + -3n = 0

Solving
5m + -3n = 0

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

Add '3n' to each side of the equation.
5m + -3n + 3n = 0 + 3n

Combine like terms: -3n + 3n = 0
5m + 0 = 0 + 3n
5m = 0 + 3n
Remove the zero:
5m = 3n

Divide each side by '5'.
m = 0.6n

Simplifying
m = 0.6n

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

Simplifying
2m + -1n = 0

Solving
2m + -1n = 0

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

Add 'n' to each side of the equation.
2m + -1n + n = 0 + n

Combine like terms: -1n + n = 0
2m + 0 = 0 + n
2m = 0 + n
Remove the zero:
2m = n

Divide each side by '2'.
m = 0.5n

Simplifying
m = 0.5n
Solution
m = {0.6n, 0.5n}

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