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 $ax^{2}+bx+c=0$.
$$2m^{2}+4m=0$$
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.
$$m=\frac{-4±\sqrt{4^{2}}}{2\times 2}$$
Take the square root of $4^{2}$.
$$m=\frac{-4±4}{2\times 2}$$
Multiply $2$ times $2$.
$$m=\frac{-4±4}{4}$$
Now solve the equation $m=\frac{-4±4}{4}$ when $±$ is plus. Add $-4$ to $4$.
$$m=\frac{0}{4}$$
Divide $0$ by $4$.
$$m=0$$
Now solve the equation $m=\frac{-4±4}{4}$ when $±$ is minus. Subtract $4$ from $-4$.
$$m=-\frac{8}{4}$$
Divide $-8$ by $4$.
$$m=-2$$
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 $x_{2}$.
$$2m^{2}+4m=2m\left(m-\left(-2\right)\right)$$
Simplify all the expressions of the form $p-\left(-q\right)$ to $p+q$.
