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[tex] (R\to C) \land (S \to C) \\

(\neg R\lor C) \land (\neg S \lor C) \ \ \ \ \ \textrm{by conditional law}\\

(\neg R\land \neg S) \lor C \ \ \ \ \textrm{by distributive law}[/tex]

I don't understand how it went from the second step to the third

my attempt from the second step was:

[tex](\neg R \land \neg S) \lor (\neg R \land C) \lor (C \land \neg S) \lor C[/tex]

but don't know where to go from here.

Did I do correctly applied the distributive law?