(a-b)+c=a(c-b)

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

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

Remove parenthesis around (a + -1b)
a + -1b + c = a(c + -1b)

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

Solving
a + -1b + c = -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.
a + -1b + ab + c = -1ab + ab + ac

Reorder the terms:
a + ab + -1b + c = -1ab + ab + ac

Combine like terms: -1ab + ab = 0
a + ab + -1b + c = 0 + ac
a + ab + -1b + c = ac

Add '-1ac' to each side of the equation.
a + ab + -1b + -1ac + c = ac + -1ac

Reorder the terms:
a + ab + -1ac + -1b + c = ac + -1ac

Combine like terms: ac + -1ac = 0
a + ab + -1ac + -1b + c = 0

Add 'b' to each side of the equation.
a + ab + -1ac + -1b + b + c = 0 + b

Combine like terms: -1b + b = 0
a + ab + -1ac + 0 + c = 0 + b
a + ab + -1ac + c = 0 + b
Remove the zero:
a + ab + -1ac + c = b

Add '-1c' to each side of the equation.
a + ab + -1ac + c + -1c = b + -1c

Combine like terms: c + -1c = 0
a + ab + -1ac + 0 = b + -1c
a + ab + -1ac = b + -1c

Reorder the terms:
a + ab + -1ac + -1b + c = b + -1b + -1c + c

Combine like terms: b + -1b = 0
a + ab + -1ac + -1b + c = 0 + -1c + c
a + ab + -1ac + -1b + c = -1c + c

Combine like terms: -1c + c = 0
a + ab + -1ac + -1b + c = 0

The solution to this equation could not be determined.