m^4-5m^3n+6m^2n^2=0

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Solution for m^4-5m^3n+6m^2n^2=0 equation: 


Simplifying
m4 + -5m3n + 6m2n2 = 0

Reorder the terms:
6m2n2 + -5m3n + m4 = 0

Solving
6m2n2 + -5m3n + m4 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), 'm2'.
m2(6n2 + -5mn + m2) = 0

Factor a trinomial.
m2((2n + -1m)(3n + -1m)) = 0


Subproblem 1
Set the factor 'm2' equal to zero and attempt to solve:

Simplifying
m2 = 0

Solving
m2 = 0

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

Simplifying
m2 = 0

Take the square root of each side:
m = {0}

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

Simplifying
2n + -1m = 0

Reorder the terms:
-1m + 2n = 0

Solving
-1m + 2n = 0

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

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

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

Divide each side by '-1'.
m = 2n

Simplifying
m = 2n

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

Simplifying
3n + -1m = 0

Reorder the terms:
-1m + 3n = 0

Solving
-1m + 3n = 0

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

Add '-3n' to each side of the equation.
-1m + 3n + -3n = 0 + -3n

Combine like terms: 3n + -3n = 0
-1m + 0 = 0 + -3n
-1m = 0 + -3n
Remove the zero:
-1m = -3n

Divide each side by '-1'.
m = 3n

Simplifying
m = 3n
Solution
m = {0, 2n, 3n}

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