\(\Leftrightarrow6-6sin^2\dfrac{x}{2}+\left(8+3\sqrt{3}\right)sin\dfrac{x}{2}-6-4\sqrt{3}=0\)
\(\Leftrightarrow-6sin^2\dfrac{x}{2}+\left(8+3\sqrt{3}\right)sin\dfrac{x}{2}-4\sqrt{3}=0\)
\(\Rightarrow\left[{}\begin{matrix}sin\dfrac{x}{2}=\dfrac{\sqrt{3}}{2}\\sin\dfrac{x}{2}=\dfrac{4}{3}>1\left(loại\right)\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\dfrac{x}{2}=\dfrac{\pi}{3}+k2\pi\\\dfrac{x}{2}=\dfrac{2\pi}{3}+k2\pi\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{2\pi}{3}+k4\pi\\x=\dfrac{4\pi}{3}+k4\pi\end{matrix}\right.\)
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