mn(m-n)(m-2n)=

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

Simplifying
mn(m + -1n)(m + -2n) = 0

Multiply (m + -1n) * (m + -2n)
mn(m(m + -2n) + -1n * (m + -2n)) = 0
mn((m * m + -2n * m) + -1n * (m + -2n)) = 0

Reorder the terms:
mn((-2mn + m2) + -1n * (m + -2n)) = 0
mn((-2mn + m2) + -1n * (m + -2n)) = 0
mn(-2mn + m2 + (m * -1n + -2n * -1n)) = 0
mn(-2mn + m2 + (-1mn + 2n2)) = 0

Reorder the terms:
mn(-2mn + -1mn + m2 + 2n2) = 0

Combine like terms: -2mn + -1mn = -3mn
mn(-3mn + m2 + 2n2) = 0
(-3mn * mn + m2 * mn + 2n2 * mn) = 0

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

Solving
2mn3 + -3m2n2 + m3n = 0

Solving for variable 'm'.

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

Factor a trinomial.
mn((n + -1m)(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 '(n + -1m)' equal to zero and attempt to solve:

Simplifying
n + -1m = 0

Reorder the terms:
-1m + n = 0

Solving
-1m + n = 0

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

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

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

Divide each side by '-1'.
m = n

Simplifying
m = n
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 = {n, 2n}