Show that \(3\sin^2{x}-2\cos{x}=1\) can be written in the form \(a\cos^2{x}+b\cos{x}+c=0\) where \(a,b\) and \(c\) are integers.
Hence, solve \(3\sin^2{x}-2\cos{x}=1\) for \(0 \leq x \leq 360^{\circ}\).
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