Answer
The solutions are $s=-1+i\sqrt{2}$ and $s=-1-i\sqrt{2}$.
Work Step by Step
$ 3s^{2}+6s+9=0\qquad$ ...divide each term with $3$.
$ s^{2}+2s+3=0\qquad$ ...add $-3$ to each side.
$ s^{2}+2s+3-3=0-3\qquad$ ...simplify.
$ s^{2}+2s=-3\qquad$ ...square half the coefficient of $s$.
$(\displaystyle \frac{2}{2})^{2}=(1)^{2}=1\qquad$ ...add $1$ to each side of the expression
$ s^{2}+2s+1=-3+1\qquad$ ...simplify.
$ s^{2}+2s+1=-2\qquad$ ... write left side as a binomial squared.
$(s+1)^{2}=-2\qquad$ ...take square roots of each side.
$ s+1=\pm\sqrt{-2}\qquad$ ...simplify.($\sqrt{-2}=i\sqrt{2}$)
$ s+1=\pm i\sqrt{2}\qquad$ ...add $-1$ to each side.
$ s+1-1=\pm i\sqrt{2}-1\qquad$ ...simplify.
$s=-1\pm i\sqrt{2}$
