(m^2-2mn)(3mn+n^2)=

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Solution for (m^2-2mn)(3mn+n^2)= equation: 


Simplifying
(m2 + -2mn)(3mn + n2) = 0

Reorder the terms:
(-2mn + m2)(3mn + n2) = 0

Multiply (-2mn + m2) * (3mn + n2)
(-2mn * (3mn + n2) + m2(3mn + n2)) = 0
((3mn * -2mn + n2 * -2mn) + m2(3mn + n2)) = 0

Reorder the terms:
((-2mn3 + -6m2n2) + m2(3mn + n2)) = 0
((-2mn3 + -6m2n2) + m2(3mn + n2)) = 0
(-2mn3 + -6m2n2 + (3mn * m2 + n2 * m2)) = 0

Reorder the terms:
(-2mn3 + -6m2n2 + (m2n2 + 3m3n)) = 0
(-2mn3 + -6m2n2 + (m2n2 + 3m3n)) = 0

Combine like terms: -6m2n2 + m2n2 = -5m2n2
(-2mn3 + -5m2n2 + 3m3n) = 0

Solving
-2mn3 + -5m2n2 + 3m3n = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), 'mn'.
mn(-2n2 + -5mn + 3m2) = 0

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


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

Simplifying
mn = 0

Solving
mn = 0

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

Simplifying
mn = 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 '(-1n + -3m)' equal to zero and attempt to solve:

Simplifying
-1n + -3m = 0

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

Solving
-3m + -1n = 0

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

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

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

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

Simplifying
m = -0.3333333333n

Subproblem 3
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
Solution
m = {-0.3333333333n, 2n}

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