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 $ax^{2}+bx+c=0$.
$$x^{2}-12x-6=0$$
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.
Now solve the equation $x=\frac{12±2\sqrt{42}}{2}$ when $±$ is plus. Add $12$ to $2\sqrt{42}$.
$$x=\frac{2\sqrt{42}+12}{2}$$
Divide $12+2\sqrt{42}$ by $2$.
$$x=\sqrt{42}+6$$
Now solve the equation $x=\frac{12±2\sqrt{42}}{2}$ when $±$ is minus. Subtract $2\sqrt{42}$ from $12$.
$$x=\frac{12-2\sqrt{42}}{2}$$
Divide $12-2\sqrt{42}$ by $2$.
$$x=6-\sqrt{42}$$
Factor the original expression using $ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right)$. Substitute $6+\sqrt{42}$ for $x_{1}$ and $6-\sqrt{42}$ for $x_{2}$.
