(m-n)(n+m)=

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

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

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

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

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

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

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

Solving
m2 + -1n2 = 0

Solving for variable 'm'.

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

Add 'n2' to each side of the equation.
m2 + -1n2 + n2 = 0 + n2

Combine like terms: -1n2 + n2 = 0
m2 + 0 = 0 + n2
m2 = 0 + n2
Remove the zero:
m2 = n2

Simplifying
m2 = n2

Take the square root of each side:
m = {-1n, n}