m^3n-10m^2n^2+24mn^3=0

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Solution for m^3n-10m^2n^2+24mn^3=0 equation: 


Simplifying
m3n + -10m2n2 + 24mn3 = 0

Reorder the terms:
24mn3 + -10m2n2 + m3n = 0

Solving
24mn3 + -10m2n2 + m3n = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), 'mn'.
mn(24n2 + -10mn + m2) = 0

Factor a trinomial.
mn((4n + -1m)(6n + -1m)) = 0


Subproblem 1
Set the factor 'mn' equal to zero and attempt to solve:

Simplifying
mn = 0

Solving
mn = 0

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

Simplifying
mn = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(4n + -1m)' equal to zero and attempt to solve:

Simplifying
4n + -1m = 0

Reorder the terms:
-1m + 4n = 0

Solving
-1m + 4n = 0

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

Add '-4n' to each side of the equation.
-1m + 4n + -4n = 0 + -4n

Combine like terms: 4n + -4n = 0
-1m + 0 = 0 + -4n
-1m = 0 + -4n
Remove the zero:
-1m = -4n

Divide each side by '-1'.
m = 4n

Simplifying
m = 4n

Subproblem 3
Set the factor '(6n + -1m)' equal to zero and attempt to solve:

Simplifying
6n + -1m = 0

Reorder the terms:
-1m + 6n = 0

Solving
-1m + 6n = 0

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

Add '-6n' to each side of the equation.
-1m + 6n + -6n = 0 + -6n

Combine like terms: 6n + -6n = 0
-1m + 0 = 0 + -6n
-1m = 0 + -6n
Remove the zero:
-1m = -6n

Divide each side by '-1'.
m = 6n

Simplifying
m = 6n
Solution
m = {4n, 6n}

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