2sinx^2-3cosx^2+sinxCosx=0

2sin^2 (x) - 3cos^2 (x) + sin (x) cos (x) = 0;

Разделим на cos^2 (x) ≠ 0;

2tg^2 (x) - 3 + tg (x) = 0;

Пусть y = tg (x);

2y^2 + y - 3 = 0;

D = 25;

y1 = (-1 + 5) / 4 = 1;

y2 = (-1 - 5) / 4 = - 3/2;

а) tg (x) = 1; x = п/4 + пn, n∈Z;

б) tg (x) = - 3/2; x = arctg (-3/2) + пk = - arctg (3/2) + пk, k∈Z.

Ответ: x = п/4 + пn, n∈Z; x = - arctg (3/2) + пk, k∈Z.