X+y’(y+xy)=0 как решить?

40+16x-2/x²-5/x³=0  |×x³                        ОДЗ: х²≠0   х³≠0   х≠0
40x³+16x⁴-2x-5=0
16x⁴+40x³-2x-5=0
x₁=0,5
16x⁴+40x³-2x-5   |_x-0,5_
16x⁴-8x³                | 16x³+48x²+22x+10

            48x³-2x
            48x³-24x²
           
                     22x²-2x
                     22x²-12x
                    
                               10x-5
                               10x-5
                               
                                        0
16x³+48x²+22x+10=0
x₂=-2,5
16x³+48x²+22x+10  |_x+2,5_
16x³+40x²                  | 16x²+8x+2

              8x²+22x
              8x²+20x
            
                        2x+10
                        2x+10
                       
                                  0
16x²+8x+2=0    |÷2
8x²+4x+1=0     D=-16  ⇒  Уравнение не имеет действительных корней.
ответ: х₁=0,5     х₂=-2,5.

Решение
1)  2cosx-1 < 0
cosx < 1/2
arccos(1/2) + 2πn < x < 2π - arccos(1/2) + 2πn, n ∈ Z
π/3 + 2πn < x < 2π - π/3 + 2πn, n ∈ Z
π/3 + 2πn < x < 5π/3 + 2πn, n ∈ Z
2)  sin2x - √2/2 < 0
 sin2x < √2/2 
- π - arcsin(√2/2) + 2πk < 2x < arcsin(√2/2) + 2πk, k ∈ Z
- π - π/4 + 2πk < 2x < π/4 + 2πk, k ∈ Z
 - 5π/4 + 2πk < 2x < π/4 + 2πk, k ∈ Z
 - 5π/8 + πk < x < π/8 + πk, k ∈ Z
3)  tgx<1
- π/2 + πn < x < arctg(1) + πn, n ∈ Z
- π/2 + πn < x < π/4 + πn, n ∈ Z