find zeroes of polynomial x square + 2x?

To find the zeroes of the given polynomial, equate it to 0 as;
$$\begin{gathered} x^2+2x = 0 \\ \Rightarrow x\left(x+2\right) = 0 \\ \Rightarrow x = 0 \mathrm{and} x = -2 \end{gathered}$$
Therefore 0 and -2 are the zeroes of the polynomial.