ax-by=a(c-b)

Solution for ax-by=a(c-b) equation:

Simplifying
ax + -1by = a(c + -1b)

Reorder the terms:
ax + -1by = a(-1b + c)
ax + -1by = (-1b * a + c * a)
ax + -1by = (-1ab + ac)

Solving
ax + -1by = -1ab + ac

Solving for variable 'a'.

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

Add 'ab' to each side of the equation.
ax + ab + -1by = -1ab + ab + ac

Reorder the terms:
ab + ax + -1by = -1ab + ab + ac

Combine like terms: -1ab + ab = 0
ab + ax + -1by = 0 + ac
ab + ax + -1by = ac

Add '-1ac' to each side of the equation.
ab + ax + -1ac + -1by = ac + -1ac

Reorder the terms:
ab + -1ac + ax + -1by = ac + -1ac

Combine like terms: ac + -1ac = 0
ab + -1ac + ax + -1by = 0

Add 'by' to each side of the equation.
ab + -1ac + ax + -1by + by = 0 + by

Combine like terms: -1by + by = 0
ab + -1ac + ax + 0 = 0 + by
ab + -1ac + ax = 0 + by
Remove the zero:
ab + -1ac + ax = by

Combine like terms: by + -1by = 0
ab + -1ac + ax + -1by = 0

The solution to this equation could not be determined.