(3y/y+3)+(9/y)+3=(27/y^2+3y)

Solution for (3y/y+3)+(9/y)+3=(27/y^2+3y) equation:

D( y )

y = 0

y^2 = 0

y = 0

y = 0

y^2 = 0

y^2 = 0

1*y^2 = 0 // : 1

y^2 = 0

y = 0

y in (-oo:0) U (0:+oo)

9/y+(3*y)/y+3+3 = 3*y+27/(y^2) // - 3*y+27/(y^2)

9/y-(3*y)-(27/(y^2))+(3*y)/y+3+3 = 0

9/y-3*y-27*y^-2+(3*y)/y+3+3 = 0

9*y^-1-3*y^1-27*y^-2+9*y^0 = 0

(9*y^2-3*y^3+9*y^1-27*y^0)/(y^2) = 0 // * y^4

y^2*(9*y^2-3*y^3+9*y^1-27*y^0) = 0

y^2

9*y^2-3*y^3+9*y-27 = 0

{ 1, -1, 3, -3, 9, -9, 27, -27 }

1

y = 1

9*y^2-3*y^3+9*y-27 = -12

1

-1

y = -1

9*y^2-3*y^3+9*y-27 = -24

-1

3

y = 3

9*y^2-3*y^3+9*y-27 = 0

3

y-3

9-3*y^2

9*y^2-3*y^3+9*y-27

y-3

3*y^3-9*y^2

9*y-27

27-9*y

0

9-3*y^2 = 0

DELTA = 0^2-(-3*4*9)

DELTA = 108

DELTA > 0

y = (108^(1/2)+0)/(-3*2) or y = (0-108^(1/2))/(-3*2)

y = -3^(1/2) or y = 3^(1/2)

y in { -3^(1/2), 3^(1/2), 3} 

y in { -3^(1/2), 3^(1/2), 3 }