mx-a-n(x-b)=nx+c

Solution for mx-a-n(x-b)=nx+c equation:

Simplifying
mx + -1a + -1n(x + -1b) = nx + c

Reorder the terms:
mx + -1a + -1n(-1b + x) = nx + c
mx + -1a + (-1b * -1n + x * -1n) = nx + c
mx + -1a + (1bn + -1nx) = nx + c

Reorder the terms:
-1a + 1bn + mx + -1nx = nx + c

Reorder the terms:
-1a + 1bn + mx + -1nx = c + nx

Solving
-1a + 1bn + mx + -1nx = c + nx

Solving for variable 'a'.

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

Add '-1bn' to each side of the equation.
-1a + 1bn + mx + -1bn + -1nx = c + -1bn + nx

Reorder the terms:
-1a + 1bn + -1bn + mx + -1nx = c + -1bn + nx

Combine like terms: 1bn + -1bn = 0
-1a + 0 + mx + -1nx = c + -1bn + nx
-1a + mx + -1nx = c + -1bn + nx

Reorder the terms:
-1a + mx + -1nx = -1bn + c + nx

Add '-1mx' to each side of the equation.
-1a + mx + -1mx + -1nx = -1bn + c + -1mx + nx

Combine like terms: mx + -1mx = 0
-1a + 0 + -1nx = -1bn + c + -1mx + nx
-1a + -1nx = -1bn + c + -1mx + nx

Add 'nx' to each side of the equation.
-1a + -1nx + nx = -1bn + c + -1mx + nx + nx

Combine like terms: -1nx + nx = 0
-1a + 0 = -1bn + c + -1mx + nx + nx
-1a = -1bn + c + -1mx + nx + nx

Combine like terms: nx + nx = 2nx
-1a = -1bn + c + -1mx + 2nx

Divide each side by '-1'.
a = bn + -1c + mx + -2nx

Simplifying
a = bn + -1c + mx + -2nx