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

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

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

Reorder the terms:
(2m + -3n)(-2m + 4n) = 0

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

Reorder the terms:
((8mn + -4m2) + -3n * (-2m + 4n)) = 0
((8mn + -4m2) + -3n * (-2m + 4n)) = 0
(8mn + -4m2 + (-2m * -3n + 4n * -3n)) = 0
(8mn + -4m2 + (6mn + -12n2)) = 0

Reorder the terms:
(8mn + 6mn + -4m2 + -12n2) = 0

Combine like terms: 8mn + 6mn = 14mn
(14mn + -4m2 + -12n2) = 0

Solving
14mn + -4m2 + -12n2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '2'.
2(7mn + -2m2 + -6n2) = 0

Factor a trinomial.
2((-2m + 3n)(m + -2n)) = 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 '(m + -2n)' equal to zero and attempt to solve:

Simplifying
m + -2n = 0

Solving
m + -2n = 0

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

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

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

Simplifying
m = 2n
Solution
m = {1.5n, 2n}