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

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

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

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

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

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

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

Solving
-5mn + m2 + -6n2 = 0

Solving for variable 'm'.

Factor a trinomial.
(m + -6n)(m + n) = 0

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

Simplifying
m + -6n = 0

Solving
m + -6n = 0

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

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

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

Simplifying
m = 6n
Subproblem 2
Set the factor '(m + n)' equal to zero and attempt to solve:

Simplifying
m + n = 0

Solving
m + n = 0

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

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

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

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