If you are asking, in terms of a procedure, when you should rearrange an equation such that one side is equal to 0, it's going to depend on the method.

In your case, you simply haven't gone far enough. If you can't factor what you have, use the quadratic formula (or completing the square). I'll factor it:

2x^2 - 7x + 6 = (2x - 3)(x - 2) = 0

x = 3/2 or x = 2

So we need y values for each of these points:

x = 3/2 ==> y = 4 - 3/2 = 5/2

x = 2 ==> y = 4 - 2 = 2

So your solutions are:

(x, y) = (3/2, 5/2)

(x, y) = (2, 2)

-Dan