Nghiệm của phương trình sin(3x - 5pi/6) + cos(3x + 3pi/4) = 0

$\begin{array}{l} \sin \left( {3x - \dfrac{{5\pi }}{6}} \right) + \cos \left( {3x + \dfrac{{3\pi }}{4}} \right) = 0\\  \Leftrightarrow \sin \left( {3x - \dfrac{{5\pi }}{6}} \right) + \cos \left( {3x + \dfrac{\pi }{2} + \dfrac{\pi }{4}} \right) = 0\\  \Leftrightarrow \sin \left( {3x - \dfrac{{5\pi }}{6}} \right) + \sin \left( { - 3x - \dfrac{\pi }{4}} \right) = 0\\  \Leftrightarrow \sin \left( {3x - \dfrac{{5\pi }}{6}} \right) - \sin \left( {3x + \dfrac{\pi }{4}} \right) = 0\\  \Leftrightarrow 2\cos \left( {3x - \dfrac{{7\pi }}{{24}}} \right)\sin \dfrac{{ - 13\pi }}{{24}} = 0\\  \Rightarrow \cos \left( {3x - \dfrac{{7\pi }}{{24}}} \right) = 0\\  \Rightarrow 3x - \dfrac{{7\pi }}{{24}} = \dfrac{\pi }{2} + k\pi \\  \Rightarrow 3x = \dfrac{{19\pi }}{{24}} + k\pi \\  \Rightarrow x = \dfrac{{19\pi }}{{72}} + k\dfrac{\pi }{3}\left( {k \in \mathbb{Z}} \right) \end{array}$