(m-n)(n-m)=

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

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

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

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

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

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

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

Solving
2mn + -1m2 + -1n2 = 0

Solving for variable 'm'.

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

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

Simplifying
-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 2
Set the factor '(m + -1n)' equal to zero and attempt to solve:

Simplifying
m + -1n = 0

Solving
m + -1n = 0

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

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

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

Simplifying
m = n
Solution
m = {n, n}