a*x+b*(x-1)=c

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

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

Multiply a * x
ax + b(x + -1) = c

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

Solving
ax + -1b + bx = c

Solving for variable 'a'.

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

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

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

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

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

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

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

Reorder the terms:
a = -1b + bx-1 + cx-1