The roots of polynomial $ p(s) $ are:
$$ \begin{aligned}s_1 &= 0\\[1 em]s_2 &= -185 \end{aligned} $$Step 1:
Factor out $ \color{blue}{ -2s }$ from $ -2s^2-370s $ and solve two separate equations:
$$ \begin{aligned} -2s^2-370s & = 0\\[1 em] \color{blue}{ -2s }\cdot ( s+185 ) & = 0 \\[1 em] \color{blue}{ -2s = 0} ~~ \text{or} ~~ s+185 & = 0 \end{aligned} $$One solution is $ \color{blue}{ s = 0 } $. Use second equation to find the remaining roots.
Step 2:
To find the second zero, solve equation $ s+185 = 0 $
$$ \begin{aligned} s+185 & = 0 \\[1 em] s & = -185 \end{aligned} $$