Which type of conic section is described by the equation \[x^2 = 2x + 2y - 3?\]Enter "C" for circle, "P" for parabola, "E" for ellipse, "H" for hyperbola, and "N" for none of the above.
Because only one of the variables appears squared (that is, there is an $x^2$ term but no $y^2$ term), this conic section must be a $\boxed{\text{(P)}}$ parabola.