y^1/3(y^4/9-5y^2/9)

Solution for y^1/3(y^4/9-5y^2/9) equation:

y in (-oo:+oo)

((y^1)/3)*((y^4)/9-((5*y^2)/9)) = 0

(y/3)*((y^4)/9+(-5/9)*y^2) = 0

1/3*y*(1/9*y^4-5/9*y^2) = 0

1/9*y^4-5/9*y^2 = 0

1/9*y^2*(y^2-5) = 0

1*y^2 = 5 // : 1

y^2 = 5

y^2 = 5 // ^ 1/2

abs(y) = 5^(1/2)

y = 5^(1/2) or y = -5^(1/2)

1/9*y^2*(y-5^(1/2))*(y+5^(1/2)) = 0

1/9*1/3*y*y^2*(y-5^(1/2))*(y+5^(1/2)) = 0

( 1/3*y )

1/3*y = 0 // : 1/3

y = 0

( 1/9*y^2 )

1/9*y^2 = 0 // : 1/9

y^2 = 0

y = 0

( y+5^(1/2) )

y+5^(1/2) = 0 // - 5^(1/2)

y = -5^(1/2)

( y-5^(1/2) )

y-5^(1/2) = 0 // + 5^(1/2)

y = 5^(1/2)

y in { 0, 0, -5^(1/2), 5^(1/2) }