Quadratic polynomial can be factored using the transformation $ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right)$, where $x_{1}$ and $x_{2}$ are the solutions of the quadratic equation $ax^{2}+bx+c=0$.
$$x^{2}+2x=0$$
All equations of the form $ax^{2}+bx+c=0$ can be solved using the quadratic formula: $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$. The quadratic formula gives two solutions, one when $±$ is addition and one when it is subtraction.
$$x=\frac{-2±\sqrt{2^{2}}}{2}$$
Take the square root of $2^{2}$.
$$x=\frac{-2±2}{2}$$
Now solve the equation $x=\frac{-2±2}{2}$ when $±$ is plus. Add $-2$ to $2$.
$$x=\frac{0}{2}$$
Divide $0$ by $2$.
$$x=0$$
Now solve the equation $x=\frac{-2±2}{2}$ when $±$ is minus. Subtract $2$ from $-2$.
$$x=-\frac{4}{2}$$
Divide $-4$ by $2$.
$$x=-2$$
Factor the original expression using $ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right)$. Substitute $0$ for $x_{1}$ and $-2$ for $x_{2}$.
$$x^{2}+2x=x\left(x-\left(-2\right)\right)$$
Simplify all the expressions of the form $p-\left(-q\right)$ to $p+q$.
