Answer
The solutions are $y=2$ and $y=\pm\dfrac{2}{3}$
Work Step by Step
$9y^{3}+8=4y+18y^{2}$
Take all terms to the left side of the equation:
$9y^{3}-18y^{2}-4y+8=0$
Group the first two terms together and the last two terms together:
$(9y^{3}-18y^{2})-(4y-8)=0$
Take out common factor $9y^{2}$ from the first group and common factor $4$ from the second group:
$9y^{2}(y-2)-4(y-2)=0$
Factor out $(y-2)$:
$(y-2)(9y^{2}-4)=0$
Set both factors equal to $0$ and solve each individual equation for $y$:
$y-2=0$
$y=2$
$9y^{2}-4=0$
$9y^{2}=4$
$y^{2}=\dfrac{4}{9}$
$\sqrt{y^{2}}=\pm\sqrt{\dfrac{4}{9}}$
$y=\pm\dfrac{2}{3}$
The solutions are $y=2$ and $y=\pm\dfrac{2}{3}$
