Ax+b=cx+b

Solution for Ax+b=cx+b equation:

Simplifying
Ax + b = cx + b

Reorder the terms:
b + xA = cx + b

Reorder the terms:
b + xA = b + cx

Add '-1b' to each side of the equation.
b + -1b + xA = b + -1b + cx

Combine like terms: b + -1b = 0
0 + xA = b + -1b + cx
xA = b + -1b + cx

Combine like terms: b + -1b = 0
xA = 0 + cx
xA = cx

Solving
xA = cx

Solving for variable 'x'.

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

Add '-1cx' to each side of the equation.
-1cx + xA = cx + -1cx

Combine like terms: cx + -1cx = 0
-1cx + xA = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-1c + A) = 0

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(-1c + A)' equal to zero and attempt to solve:

Simplifying
-1c + A = 0

Reorder the terms:
A + -1c = 0

Solving
A + -1c = 0

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

Add '-1A' to each side of the equation.
A + -1A + -1c = 0 + -1A

Combine like terms: A + -1A = 0
0 + -1c = 0 + -1A
-1c = 0 + -1A
Remove the zero:
-1c = -1A

Add 'c' to each side of the equation.
-1c + c = -1A + c

Combine like terms: -1c + c = 0
0 = -1A + c

Simplifying
0 = -1A + c

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}