\(\Leftrightarrow3\cdot\dfrac{1-cos2x}{2}+sin2x+5\cdot\dfrac{1+cos2x}{2}=3\)
\(\Leftrightarrow\dfrac{3}{2}-\dfrac{3}{2}cos2x+sin2x+\dfrac{5}{2}+\dfrac{5}{2}cos2x=3\)
\(\Leftrightarrow sin2x+cos2x=-1\)
\(\Leftrightarrow sin\left(2x+\dfrac{\Pi}{4}\right)=-\dfrac{1}{\sqrt{2}}\)
\(\Leftrightarrow\left[{}\begin{matrix}2x+\dfrac{\Pi}{4}=-\dfrac{\Pi}{4}+k2\Pi\\2x=\dfrac{5}{4}\Pi+k2\Pi\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=-\dfrac{1}{4}\Pi+k\Pi\\x=\dfrac{5}{8}\Pi+k\Pi\end{matrix}\right.\)
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