(M+x)(n-m)=1

Solution for (M+x)(n-m)=1 equation:

Simplifying
(M + x)(n + -1m) = 1

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

Multiply (M + x) * (-1m + n)
(M(-1m + n) + x(-1m + n)) = 1
((-1m * M + n * M) + x(-1m + n)) = 1
((-1mM + nM) + x(-1m + n)) = 1
(-1mM + nM + (-1m * x + n * x)) = 1
(-1mM + nM + (-1mx + nx)) = 1

Reorder the terms:
(-1mM + -1mx + nM + nx) = 1
(-1mM + -1mx + nM + nx) = 1

Solving
-1mM + -1mx + nM + nx = 1

Solving for variable 'm'.

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

Add '-1nM' to each side of the equation.
-1mM + -1mx + nM + -1nM + nx = 1 + -1nM

Combine like terms: nM + -1nM = 0
-1mM + -1mx + 0 + nx = 1 + -1nM
-1mM + -1mx + nx = 1 + -1nM

Add '-1nx' to each side of the equation.
-1mM + -1mx + nx + -1nx = 1 + -1nM + -1nx

Combine like terms: nx + -1nx = 0
-1mM + -1mx + 0 = 1 + -1nM + -1nx
-1mM + -1mx = 1 + -1nM + -1nx

Reorder the terms:
-1 + -1mM + -1mx + nM + nx = 1 + -1nM + -1nx + -1 + nM + nx

Reorder the terms:
-1 + -1mM + -1mx + nM + nx = 1 + -1 + -1nM + nM + -1nx + nx

Combine like terms: 1 + -1 = 0
-1 + -1mM + -1mx + nM + nx = 0 + -1nM + nM + -1nx + nx
-1 + -1mM + -1mx + nM + nx = -1nM + nM + -1nx + nx

Combine like terms: -1nM + nM = 0
-1 + -1mM + -1mx + nM + nx = 0 + -1nx + nx
-1 + -1mM + -1mx + nM + nx = -1nx + nx

Combine like terms: -1nx + nx = 0
-1 + -1mM + -1mx + nM + nx = 0

The solution to this equation could not be determined.