Expand the products on both sides:
[tex]a(y+c)=b(y-c) \implies ay+ac=by-bc[/tex]
Move all terms containing y to one side:
[tex]ay+ac=by-bc \implies ay-by=-ac-bc[/tex]
Factor out y :
[tex]ay-by=-ac-bc \implies y(a-b)=-ac-bc[/tex]
Solve for y :
[tex]y(a-b)=-ac-bc \implies y=\dfrac{-ac-bc}{a-b}=-\dfrac{c(a+b)}{a-b}=\dfrac{c(a+b)}{b-a}[/tex]
