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 $ax^{2}+bx+c=0$.
$$4x^{2}+2x=0$$
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.
$$x=\frac{-2±\sqrt{2^{2}}}{2\times 4}$$
Take the square root of $2^{2}$.
$$x=\frac{-2±2}{2\times 4}$$
Multiply $2$ times $4$.
$$x=\frac{-2±2}{8}$$
Now solve the equation $x=\frac{-2±2}{8}$ when $±$ is plus. Add $-2$ to $2$.
$$x=\frac{0}{8}$$
Divide $0$ by $8$.
$$x=0$$
Now solve the equation $x=\frac{-2±2}{8}$ when $±$ is minus. Subtract $2$ from $-2$.
$$x=-\frac{4}{8}$$
Reduce the fraction $\frac{-4}{8}$ to lowest terms by extracting and canceling out $4$.
$$x=-\frac{1}{2}$$
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 $-\frac{1}{2}$ for $x_{2}$.
