=15m^6n+14m^5n+3m^4n^3

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Solution for =15m^6n+14m^5n+3m^4n^3 equation: 


Simplifying
0 = 15m6n + 14m5n + 3m4n3

Reorder the terms:
0 = 3m4n3 + 14m5n + 15m6n

Solving
0 = 3m4n3 + 14m5n + 15m6n

Solving for variable 'm'.
Remove the zero:
-3m4n3 + -14m5n + -15m6n = 3m4n3 + 14m5n + 15m6n + -3m4n3 + -14m5n + -15m6n

Reorder the terms:
-3m4n3 + -14m5n + -15m6n = 3m4n3 + -3m4n3 + 14m5n + -14m5n + 15m6n + -15m6n

Combine like terms: 3m4n3 + -3m4n3 = 0
-3m4n3 + -14m5n + -15m6n = 0 + 14m5n + -14m5n + 15m6n + -15m6n
-3m4n3 + -14m5n + -15m6n = 14m5n + -14m5n + 15m6n + -15m6n

Combine like terms: 14m5n + -14m5n = 0
-3m4n3 + -14m5n + -15m6n = 0 + 15m6n + -15m6n
-3m4n3 + -14m5n + -15m6n = 15m6n + -15m6n

Combine like terms: 15m6n + -15m6n = 0
-3m4n3 + -14m5n + -15m6n = 0

Factor out the Greatest Common Factor (GCF), '-1m4n'.
-1m4n(3n2 + 14m + 15m2) = 0

Factor a trinomial.
-1m4n((3n + 5m)(n + 3m)) = 0

Ignore the factor -1.

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 '(3n + 5m)' equal to zero and attempt to solve:

Simplifying
3n + 5m = 0

Reorder the terms:
5m + 3n = 0

Solving
5m + 3n = 0

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

Add '-3n' to each side of the equation.
5m + 3n + -3n = 0 + -3n

Combine like terms: 3n + -3n = 0
5m + 0 = 0 + -3n
5m = 0 + -3n
Remove the zero:
5m = -3n

Divide each side by '5'.
m = -0.6n

Simplifying
m = -0.6n

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

Simplifying
n + 3m = 0

Reorder the terms:
3m + n = 0

Solving
3m + n = 0

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

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

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

Divide each side by '3'.
m = -0.3333333333n

Simplifying
m = -0.3333333333n
Solution
m = {-0.6n, -0.3333333333n}

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