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 $ax^{2}+bx+c=0$.
$$x^{2}+12x=0$$
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.
$$x=\frac{-12±\sqrt{12^{2}}}{2}$$
Take the square root of $12^{2}$.
$$x=\frac{-12±12}{2}$$
Now solve the equation $x=\frac{-12±12}{2}$ when $±$ is plus. Add $-12$ to $12$.
$$x=\frac{0}{2}$$
Divide $0$ by $2$.
$$x=0$$
Now solve the equation $x=\frac{-12±12}{2}$ when $±$ is minus. Subtract $12$ from $-12$.
$$x=-\frac{24}{2}$$
Divide $-24$ by $2$.
$$x=-12$$
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 $-12$ for $x_{2}$.
$$x^{2}+12x=x\left(x-\left(-12\right)\right)$$
Simplify all the expressions of the form $p-\left(-q\right)$ to $p+q$.
