-42m^6n+49m^5n^2+21m^4n^3=

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Solution for -42m^6n+49m^5n^2+21m^4n^3= equation: 


Simplifying
-42m6n + 49m5n2 + 21m4n3 = 0

Reorder the terms:
21m4n3 + 49m5n2 + -42m6n = 0

Solving
21m4n3 + 49m5n2 + -42m6n = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '7m4n'.
7m4n(3n2 + 7mn + -6m2) = 0

Factor a trinomial.
7m4n((3n + -2m)(n + 3m)) = 0

Ignore the factor 7.

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 + -2m)' equal to zero and attempt to solve:

Simplifying
3n + -2m = 0

Reorder the terms:
-2m + 3n = 0

Solving
-2m + 3n = 0

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

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

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

Divide each side by '-2'.
m = 1.5n

Simplifying
m = 1.5n

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 = {1.5n, -0.3333333333n}

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