(x+m)2-(x+n)2=(m-m)2

Solution for (x+m)2-(x+n)2=(m-m)2 equation:

Simplifying
(x + m) * 2 + -1(x + n) * 2 = (m + -1m) * 2

Reorder the terms:
(m + x) * 2 + -1(x + n) * 2 = (m + -1m) * 2

Reorder the terms for easier multiplication:
2(m + x) + -1(x + n) * 2 = (m + -1m) * 2
(m * 2 + x * 2) + -1(x + n) * 2 = (m + -1m) * 2
(2m + 2x) + -1(x + n) * 2 = (m + -1m) * 2

Reorder the terms:
2m + 2x + -1(n + x) * 2 = (m + -1m) * 2

Reorder the terms for easier multiplication:
2m + 2x + -1 * 2(n + x) = (m + -1m) * 2

Multiply -1 * 2
2m + 2x + -2(n + x) = (m + -1m) * 2
2m + 2x + (n * -2 + x * -2) = (m + -1m) * 2
2m + 2x + (-2n + -2x) = (m + -1m) * 2

Reorder the terms:
2m + -2n + 2x + -2x = (m + -1m) * 2

Combine like terms: 2x + -2x = 0
2m + -2n + 0 = (m + -1m) * 2
2m + -2n = (m + -1m) * 2

Combine like terms: m + -1m = 0
2m + -2n = (0) * 2

Multiply 0 * 2
2m + -2n = 0

Anything times zero is zero.
2m + -2n = 0

Solving
2m + -2n = 0

Solving for variable 'm'.

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

Add '2n' to each side of the equation.
2m + -2n + 2n = 0 + 2n

Combine like terms: -2n + 2n = 0
2m + 0 = 0 + 2n
2m = 0 + 2n
Remove the zero:
2m = 2n

Divide each side by '2'.
m = n

Simplifying
m = n