5sin2x + 3sinx - 2 =0

$\begin{array}{l} 5{\sin ^2}x + 3\sin x - 2 = 0 \Leftrightarrow \left( {\sin x - 1} \right)\left( {5\sin x + 2} \right) = 0\\ \Leftrightarrow \left[ \begin{array}{l} \sin x = 1\\ \sin x = - \frac{2}{5} \end{array} \right. \Leftrightarrow \left[ \begin{array}{l} x = \frac{\pi }{2} + k2\pi \\ x = \arcsin \left( { - \frac{2}{5}} \right) + k2\pi \\ x = \pi - \arcsin \left( { - \frac{2}{5}} \right) + k2\pi \end{array} \right. \end{array}$