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

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

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

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

Reorder the terms:
a + -1b + c = a + c(-1b + c)
a + -1b + c = a + (-1b * c + c * c)
a + -1b + c = a + (-1bc + c2)

Add '-1a' to each side of the equation.
a + -1b + -1a + c = a + -1bc + -1a + c2

Reorder the terms:
a + -1a + -1b + c = a + -1bc + -1a + c2

Combine like terms: a + -1a = 0
0 + -1b + c = a + -1bc + -1a + c2
-1b + c = a + -1bc + -1a + c2

Reorder the terms:
-1b + c = a + -1a + -1bc + c2

Combine like terms: a + -1a = 0
-1b + c = 0 + -1bc + c2
-1b + c = -1bc + c2

Solving
-1b + c = -1bc + c2

Solving for variable 'b'.

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

Add 'bc' to each side of the equation.
-1b + bc + c = -1bc + bc + c2

Combine like terms: -1bc + bc = 0
-1b + bc + c = 0 + c2
-1b + bc + c = c2

Add '-1c' to each side of the equation.
-1b + bc + c + -1c = -1c + c2

Combine like terms: c + -1c = 0
-1b + bc + 0 = -1c + c2
-1b + bc = -1c + c2

Reorder the terms:
-1b + bc + c + -1c2 = -1c + c + c2 + -1c2

Combine like terms: -1c + c = 0
-1b + bc + c + -1c2 = 0 + c2 + -1c2
-1b + bc + c + -1c2 = c2 + -1c2

Combine like terms: c2 + -1c2 = 0
-1b + bc + c + -1c2 = 0

The solution to this equation could not be determined.