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