10m^6n+27m^5n^2+5m^4n^3=0

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Solution for 10m^6n+27m^5n^2+5m^4n^3=0 equation: 


Simplifying
10m6n + 27m5n2 + 5m4n3 = 0

Reorder the terms:
5m4n3 + 27m5n2 + 10m6n = 0

Solving
5m4n3 + 27m5n2 + 10m6n = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), 'm4n'.
m4n(5n2 + 27mn + 10m2) = 0

Factor a trinomial.
m4n((5n + 2m)(n + 5m)) = 0


Subproblem 1
Set the factor 'm4n' equal to zero and attempt to solve:

Simplifying
m4n = 0

Solving
m4n = 0

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

Simplifying
m4n = 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 '(5n + 2m)' equal to zero and attempt to solve:

Simplifying
5n + 2m = 0

Reorder the terms:
2m + 5n = 0

Solving
2m + 5n = 0

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

Add '-5n' to each side of the equation.
2m + 5n + -5n = 0 + -5n

Combine like terms: 5n + -5n = 0
2m + 0 = 0 + -5n
2m = 0 + -5n
Remove the zero:
2m = -5n

Divide each side by '2'.
m = -2.5n

Simplifying
m = -2.5n

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

Simplifying
n + 5m = 0

Reorder the terms:
5m + n = 0

Solving
5m + n = 0

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

Add '-1n' to each side of the equation.
5m + n + -1n = 0 + -1n

Combine like terms: n + -1n = 0
5m + 0 = 0 + -1n
5m = 0 + -1n
Remove the zero:
5m = -1n

Divide each side by '5'.
m = -0.2n

Simplifying
m = -0.2n
Solution
m = {-2.5n, -0.2n}

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