The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0\\[1 em]x_2 &= -\frac{ 7 }{ 4 }+\frac{\sqrt{ 23 }}{ 4 }i\\[1 em]x_3 &= -\frac{ 7 }{ 4 }- \frac{\sqrt{ 23 }}{ 4 }i \end{aligned} $$Step 1:
Factor out $ \color{blue}{ x }$ from $ 2x^3+7x^2+9x $ and solve two separate equations:
$$ \begin{aligned} 2x^3+7x^2+9x & = 0\\[1 em] \color{blue}{ x }\cdot ( 2x^2+7x+9 ) & = 0 \\[1 em] \color{blue}{ x = 0} ~~ \text{or} ~~ 2x^2+7x+9 & = 0 \end{aligned} $$One solution is $ \color{blue}{ x = 0 } $. Use second equation to find the remaining roots.
Step 2:
The solutions of $ 2x^2+7x+9 = 0 $ are: $ x = -\dfrac{ 7 }{ 4 }+\dfrac{\sqrt{ 23 }}{ 4 }i ~ \text{and} ~ x = -\dfrac{ 7 }{ 4 }-\dfrac{\sqrt{ 23 }}{ 4 }i$.
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