help with equivalence relations in real numbers

Question

Let S be a relation in $\mathbb{R}$ defined by: xSy iff $x^2-y^2=3x-3y$.

a) Prove that S is equivalence relation.

b) Find [a]$_S$ (for $a \in \mathbb{R}$ arbitrary).

c) Describe $\mathbb{R}$/S.

I need help in particular for b), but any suggestions for others is welcome.

S is an equivalence relation if S is reflexive, symmetric and transitive.

S is reflexive for all x in $\mathbb{R}$: $x^2-x^2=0=3x-3x$.

S is symmetric for all x and y if xSy then $x^2-y^2=3x-3y$ then $-(y^2-x^2)=-(3y-3x)$, hence $y^2-x^2=3y-3x$, therefore ySx.

Answer 1

Note that $x^2-y^2=(x-y)(x+y)$; so, this is equivalent to $$ (x-y)(x+y)=3(x-y), $$ or $$ (x-y)(x+y-3)=0. $$ When $x=a$ , what values of $y$ satisfy this relation?