c*x+a*b=c-1

Solution for c*x+a*b=c-1 equation:

Simplifying
c * x + a * b = c + -1

Multiply c * x
cx + a * b = c + -1

Multiply a * b
cx + ab = c + -1

Reorder the terms:
ab + cx = c + -1

Reorder the terms:
ab + cx = -1 + c

Solving
ab + cx = -1 + c

Solving for variable 'a'.

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

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

Combine like terms: cx + -1cx = 0
ab + 0 = -1 + c + -1cx
ab = -1 + c + -1cx

Divide each side by 'b'.
a = -1b-1 + b-1c + -1b-1cx

Simplifying
a = -1b-1 + b-1c + -1b-1cx