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

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

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

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

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

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

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