The equation of a curve is such that \(\frac{dy}{dx} = 6x^2 - 30x + 6a\), where \(a\) is a positive constant. The curve has a stationary point at \((a, -15)\).

(a) Find the value of \(a\).

(b) Determine the nature of this stationary point.

(c) Find the equation of the curve.

(d) Find the coordinates of any other stationary points on the curve.