6sin²x + sinxcosx - cos²x = 0

6sin^2x+sinxcosx-cos^2x=0

- (cosx-3sinx) (cosx+2sinx) = 0

(cosx-3sinx) (cosx+2sinx) = 0

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

ctgx=3 2sinx=-cosx

x=arcctg (3) + πn; n∈Z 2tgx=-1

tgx=-1/2

x=arctg (-1/2) + πn; n∈Z

Разделим на cos²x≠0

6tg²x+tgx-1=0

tgx=a

6a²+a-1=0

D=1+24=25

a1 = (-1-5) / 12=-1/2⇒tgx=-1/2⇒x=-arctg1/2+πn

a2 = (-1+5) / 12=1/3⇒tgx=1/3⇒x=arctg1/3+πn