Решите однородные тригонометрические уравнения

2sin^2x - 4 = 3sinxcosx - 4cos^2x
2sin^2x - 4 × 1 - 3sinxcosx + 4cos^2x = 0
[ sin^2a + cos^2a = 1 ]
2sin^2x - 4 × ( sin^2x + cos^2x) - 3sinxcosx + 4cos^2x = 0
2sin^2x - 4sin^2x - 4cos^2x - 3sinxcosx + 4cos^2x = 0 | : cos^2x
2tg^2x - 4tg^2x - 4 - 3tgx + 4 = 0
- 2tg^2x - 3tgx = 0 | × (-1)
2tg^2x + 3tgx = 0
tgx ( 2tgx + 3) = 0
tgx = 0
x1 = Пn, n € Z
2tgx + 3 = 0
2tgx = -3 | :2
tgx = -3/2
x = arctg (-3/2) + Пn, n € Z
x = - arctg 3/2 + Пn, n € Z