mn(m-6n)(m+n)=

Solution for mn(m-6n)(m+n)= equation:

Simplifying
mn(m + -6n)(m + n) = 0

Multiply (m + -6n) * (m + n)
mn(m(m + n) + -6n * (m + n)) = 0
mn((m * m + n * m) + -6n * (m + n)) = 0

Reorder the terms:
mn((mn + m2) + -6n * (m + n)) = 0
mn((mn + m2) + -6n * (m + n)) = 0
mn(mn + m2 + (m * -6n + n * -6n)) = 0
mn(mn + m2 + (-6mn + -6n2)) = 0

Reorder the terms:
mn(mn + -6mn + m2 + -6n2) = 0

Combine like terms: mn + -6mn = -5mn
mn(-5mn + m2 + -6n2) = 0
(-5mn * mn + m2 * mn + -6n2 * mn) = 0

Reorder the terms:
(-6mn3 + -5m2n2 + m3n) = 0
(-6mn3 + -5m2n2 + m3n) = 0

Solving
-6mn3 + -5m2n2 + m3n = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), 'mn'.
mn(-6n2 + -5mn + m2) = 0

Factor a trinomial.
mn((-1n + -1m)(6n + -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 + -1m)' equal to zero and attempt to solve:

Simplifying
-1n + -1m = 0

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

Solving
-1m + -1n = 0

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

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

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

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

Simplifying
m = -1n
Subproblem 3
Set the factor '(6n + -1m)' equal to zero and attempt to solve:

Simplifying
6n + -1m = 0

Reorder the terms:
-1m + 6n = 0

Solving
-1m + 6n = 0

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

Add '-6n' to each side of the equation.
-1m + 6n + -6n = 0 + -6n

Combine like terms: 6n + -6n = 0
-1m + 0 = 0 + -6n
-1m = 0 + -6n
Remove the zero:
-1m = -6n

Divide each side by '-1'.
m = 6n

Simplifying
m = 6n
Solution
m = {-1n, 6n}