6m^6n+7m^5n^2+2m^4n^3=0

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Solution for 6m^6n+7m^5n^2+2m^4n^3=0 equation: 


Simplifying
6m6n + 7m5n2 + 2m4n3 = 0

Reorder the terms:
2m4n3 + 7m5n2 + 6m6n = 0

Solving
2m4n3 + 7m5n2 + 6m6n = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), 'm4n'.
m4n(2n2 + 7mn + 6m2) = 0

Factor a trinomial.
m4n((2n + 3m)(n + 2m)) = 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 '(2n + 3m)' equal to zero and attempt to solve:

Simplifying
2n + 3m = 0

Reorder the terms:
3m + 2n = 0

Solving
3m + 2n = 0

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

Add '-2n' to each side of the equation.
3m + 2n + -2n = 0 + -2n

Combine like terms: 2n + -2n = 0
3m + 0 = 0 + -2n
3m = 0 + -2n
Remove the zero:
3m = -2n

Divide each side by '3'.
m = -0.6666666667n

Simplifying
m = -0.6666666667n

Subproblem 3
Set the factor '(n + 2m)' equal to zero and attempt to solve:

Simplifying
n + 2m = 0

Reorder the terms:
2m + n = 0

Solving
2m + n = 0

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

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

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

Divide each side by '2'.
m = -0.5n

Simplifying
m = -0.5n
Solution
m = {-0.6666666667n, -0.5n}

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