ax-b=(1-b)x+3b

Solution for ax-b=(1-b)x+3b equation:

Simplifying
ax + -1b = (1 + -1b) * x + 3b

Reorder the terms for easier multiplication:
ax + -1b = x(1 + -1b) + 3b
ax + -1b = (1 * x + -1b * x) + 3b

Reorder the terms:
ax + -1b = (-1bx + 1x) + 3b
ax + -1b = (-1bx + 1x) + 3b

Reorder the terms:
ax + -1b = 3b + -1bx + 1x

Solving
ax + -1b = 3b + -1bx + 1x

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 = 3b + -1bx + b + 1x

Combine like terms: -1b + b = 0
ax + 0 = 3b + -1bx + b + 1x
ax = 3b + -1bx + b + 1x

Reorder the terms:
ax = 3b + b + -1bx + 1x

Combine like terms: 3b + b = 4b
ax = 4b + -1bx + 1x

Divide each side by 'x'.
a = 4bx-1 + -1b + 1

Simplifying
a = 4bx-1 + -1b + 1

Reorder the terms:
a = 1 + -1b + 4bx-1