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 $ax^{2}+bx+c=0$.
$$4x^{2}+8x=0$$
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.
$$x=\frac{-8±\sqrt{8^{2}}}{2\times 4}$$
Take the square root of $8^{2}$.
$$x=\frac{-8±8}{2\times 4}$$
Multiply $2$ times $4$.
$$x=\frac{-8±8}{8}$$
Now solve the equation $x=\frac{-8±8}{8}$ when $±$ is plus. Add $-8$ to $8$.
$$x=\frac{0}{8}$$
Divide $0$ by $8$.
$$x=0$$
Now solve the equation $x=\frac{-8±8}{8}$ when $±$ is minus. Subtract $8$ from $-8$.
$$x=-\frac{16}{8}$$
Divide $-16$ by $8$.
$$x=-2$$
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 $x_{2}$.
$$4x^{2}+8x=4x\left(x-\left(-2\right)\right)$$
Simplify all the expressions of the form $p-\left(-q\right)$ to $p+q$.
