9sin2x - 30sinx.cosx + 25cos2x = 25
$9\sin^2 x - 30\sin x \cos x - 25(1-\cos^2 x) = 0$
$\Leftrightarrow 9\sin^2 x -30\sin x \cos x-25\sin^2 x=0$
$\Leftrightarrow 16\sin^2 x + 30\sin x \cos x = 0$
$\Leftrightarrow \sin x (8\sin x + 15\cos x) = 0$
+ $\sin x = 0 \Rightarrow x= k\pi;\ k \in Z$
+ $8\sin x + 15\cos x =0$
$\Leftrightarrow 8\tan x + 15 = 0$
$\Leftrightarrow \tan x = -\dfrac{15}{8} \Rightarrow x = arc \tan(-\dfrac{15}{8}) + k\pi;\ k \in Z$