\section*{Problem 2 - 091212}

a) All real solutions of the equation \(x(x+1)(x+2)(x+3)=\frac{9}{16}\) are to be determined.

b) Furthermore, all real numbers \(a\) are to be specified for which the equation \(x(x+1)(x+2)(x+3)=a\) has no, exactly one, exactly two, exactly three, exactly four, or more than four different real solutions in \(x\).