The function \(f\) is defined by

\(f(x)=(2x+1)(3x-2)^2\).

(a) Show that \(f'(x)\) can be written in the form \(2(3x-2)(px+q)\), where \(p\) and \(q\) are integers to be found.

(b) Find the coordinates of the stationary points of the graph of \(y=f(x)\).

(c) Sketch the graph of \(y=f(x)\), showing clearly the intercepts with the axes and the stationary points.

(d) Find the set of values of the constant \(k\) for which the equation \(f(x)=k\) has 3 distinct real roots.