Probabilities of two independent events expressed in terms of a parameter

The events \(C\) and \(D\) are such that \(P(C\cap D)=\frac{10-x}{15}\), \(P(C'\cap D)=\frac15\) and \(P(C\cap D')=\frac{4+x}{30}\), where \(0\leq x\leq10\).

1. Show that \(P(C)=\frac{24-x}{30}\).[3]
2. The events \(C\) and \(D\) are now known to be independent.
   Find all possible values of \(x\).[6]