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

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


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

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

Reorder the terms:
((-8mn + 6m2) + -3n * (3m + -4n)) = 0
((-8mn + 6m2) + -3n * (3m + -4n)) = 0
(-8mn + 6m2 + (3m * -3n + -4n * -3n)) = 0
(-8mn + 6m2 + (-9mn + 12n2)) = 0

Reorder the terms:
(-8mn + -9mn + 6m2 + 12n2) = 0

Combine like terms: -8mn + -9mn = -17mn
(-17mn + 6m2 + 12n2) = 0

Solving
-17mn + 6m2 + 12n2 = 0

Solving for variable 'm'.

Factor a trinomial.
(2m + -3n)(3m + -4n) = 0


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 '(3m + -4n)' equal to zero and attempt to solve:

Simplifying
3m + -4n = 0

Solving
3m + -4n = 0

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

Add '4n' to each side of the equation.
3m + -4n + 4n = 0 + 4n

Combine like terms: -4n + 4n = 0
3m + 0 = 0 + 4n
3m = 0 + 4n
Remove the zero:
3m = 4n

Divide each side by '3'.
m = 1.333333333n

Simplifying
m = 1.333333333n
Solution
m = {1.5n, 1.333333333n}

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