a(x-2)-b(x-1)=b-a

Solution for a(x-2)-b(x-1)=b-a equation:

Simplifying
a(x + -2) + -1b(x + -1) = b + -1a

Reorder the terms:
a(-2 + x) + -1b(x + -1) = b + -1a
(-2 * a + x * a) + -1b(x + -1) = b + -1a
(-2a + ax) + -1b(x + -1) = b + -1a

Reorder the terms:
-2a + ax + -1b(-1 + x) = b + -1a
-2a + ax + (-1 * -1b + x * -1b) = b + -1a
-2a + ax + (1b + -1bx) = b + -1a

Reorder the terms:
-2a + ax + 1b + -1bx = -1a + b

Solving
-2a + ax + 1b + -1bx = -1a + b

Solving for variable 'a'.

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

Add 'a' to each side of the equation.
-2a + ax + 1b + a + -1bx = -1a + a + b

Reorder the terms:
-2a + a + ax + 1b + -1bx = -1a + a + b

Combine like terms: -2a + a = -1a
-1a + ax + 1b + -1bx = -1a + a + b

Combine like terms: -1a + a = 0
-1a + ax + 1b + -1bx = 0 + b
-1a + ax + 1b + -1bx = b

Add '-1b' to each side of the equation.
-1a + ax + 1b + -1b + -1bx = b + -1b

Combine like terms: 1b + -1b = 0
-1a + ax + 0 + -1bx = b + -1b
-1a + ax + -1bx = b + -1b

Combine like terms: b + -1b = 0
-1a + ax + -1bx = 0

Add 'bx' to each side of the equation.
-1a + ax + -1bx + bx = 0 + bx

Combine like terms: -1bx + bx = 0
-1a + ax + 0 = 0 + bx
-1a + ax = 0 + bx
Remove the zero:
-1a + ax = bx

Combine like terms: bx + -1bx = 0
-1a + ax + -1bx = 0

The solution to this equation could not be determined.