6sin^2+sinx * cosx - cos^2x=0

6sin^2 (x) + sin (x) cos (x) - cos^2 (x) = 0;

Разделим обе части на cos^2 (x) ≠ 0;

6tg^2 (x) + tg (x) - 1 = 0;

Сделаем замену переменной: tg (x) = t;

6t^2 + t - 1 = 0;

D = 25;

t1 = (-1 + 5) / 12 = 1/3;

t2 = (-1 - 5) / 12 = - 1/2;

tg (x) = 1/3 = => x = arctg (1/3) + пk, k∈Z.

tg (x) = - 1/2 = => x = - arctg (1/2) + пn, n∈Z.

Ответ: x = arctg (1/3) + пk, k∈Z; x = - arctg (1/2) + пn, n∈Z.