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

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

Simplifying
a(X + b) = b(X + -1c)
(X * a + b * a) = b(X + -1c)
(aX + ab) = b(X + -1c)
aX + ab = (X * b + -1c * b)
aX + ab = (bX + -1bc)

Solving
aX + ab = bX + -1bc

Solving for variable 'a'.

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

Reorder the terms:
aX + ab + -1bX + bc = bX + -1bX + -1bc + bc

Combine like terms: bX + -1bX = 0
aX + ab + -1bX + bc = 0 + -1bc + bc
aX + ab + -1bX + bc = -1bc + bc

Combine like terms: -1bc + bc = 0
aX + ab + -1bX + bc = 0

The solution to this equation could not be determined.