Answer:
y = 0 or y = -2/3
Step-by-step explanation:
[tex]3y^3\left(y^2+\dfrac{2}{3}y\right)=0[/tex]
The product is zero if one of the factors is equal to zero. Therefore
[tex]3y^3\left(y^2+\dfrac{2}{3}y\right)=0\iff3y^3=0\ \vee\ y^2+\dfrac{2}{3}y=0\\\\3y^3=0\qquad\text{divide both sides by 3}\\\\y^3=0\to \boxed{y=0}\\\\y^2+\dfrac{2}{3}y=0\\\\y\left(y+\dfrac{2}{3}\right)=0\iff y=0\ \vee\ y+\dfrac{2}{3}=0\to \boxed{y=-\dfrac{2}{3}}[/tex]
