Consider,

\[S = 2 \left [1+x+\sum_{k=1}^{\infty}{ \left(\dfrac{x^{(4k)}}{(4k)!}+\dfrac{x^{(4k+1)}}{(4k+1)!} \right)} \right ] \]

If \(S=0\), then find all possible numbers of solution for \(-6 < x < 0\).

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