32. 6 cos 2x (2 cos x + √2) = 0.

1) $$cos 2x = 0$$

$$2x = \frac{\pi}{2} + \pi n, n \in Z$$

$$x = \frac{\pi}{4} + \frac{\pi n}{2}, n \in Z$$

2) $$2 cos x + \sqrt{2} = 0$$

$$cos x = -\frac{\sqrt{2}}{2}$$

$$x = \pm \frac{3\pi}{4} + 2\pi n, n \in Z$$

Ответ: $$x = \frac{\pi}{4} + \frac{\pi n}{2}, x = \pm \frac{3\pi}{4} + 2\pi n, n \in Z$$