Given that \(f(x)=x^2-4\) and \(g(x)=x+3\), what are all the values of \(x\) for which \(f(g(x))=0\) ?

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$$ f(g(x))=0 $$ $$ (x+3)^2-4 =0 $$ $$ (x+3)^2 = 4 $$ $$ (x+3)= \pm 2 $$ $$ x=-1 \text{ and } x=-5 $$