ax+b=c-a(x-b)

Solution for ax+b=c-a(x-b) equation:

Simplifying
ax + b = c + -1a(x + -1b)

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

Reorder the terms:
ax + b = 1ab + -1ax + c

Solving
ax + b = 1ab + -1ax + c

Solving for variable 'a'.

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

Add '-1ab' to each side of the equation.
ax + -1ab + b = 1ab + -1ax + -1ab + c

Reorder the terms:
-1ab + ax + b = 1ab + -1ax + -1ab + c

Reorder the terms:
-1ab + ax + b = 1ab + -1ab + -1ax + c

Combine like terms: 1ab + -1ab = 0
-1ab + ax + b = 0 + -1ax + c
-1ab + ax + b = -1ax + c

Add 'ax' to each side of the equation.
-1ab + ax + ax + b = -1ax + ax + c

Combine like terms: ax + ax = 2ax
-1ab + 2ax + b = -1ax + ax + c

Combine like terms: -1ax + ax = 0
-1ab + 2ax + b = 0 + c
-1ab + 2ax + b = c

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

Combine like terms: b + -1b = 0
-1ab + 2ax + 0 = -1b + c
-1ab + 2ax = -1b + c

Reorder the terms:
-1ab + 2ax + b + -1c = -1b + b + c + -1c

Combine like terms: -1b + b = 0
-1ab + 2ax + b + -1c = 0 + c + -1c
-1ab + 2ax + b + -1c = c + -1c

Combine like terms: c + -1c = 0
-1ab + 2ax + b + -1c = 0

The solution to this equation could not be determined.