Combine $-6x^{2}$ and $-5x^{2}$ to get $-11x^{2}$.
$$factor(-11x^{2}+7x-2+6+12x)$$
Add $-2$ and $6$ to get $4$.
$$factor(-11x^{2}+7x+4+12x)$$
Combine $7x$ and $12x$ to get $19x$.
$$factor(-11x^{2}+19x+4)$$
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 $ax^{2}+bx+c=0$.
$$-11x^{2}+19x+4=0$$
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 $x=\frac{-19±\sqrt{537}}{-22}$ when $±$ is plus. Add $-19$ to $\sqrt{537}$.
$$x=\frac{\sqrt{537}-19}{-22}$$
Divide $-19+\sqrt{537}$ by $-22$.
$$x=\frac{19-\sqrt{537}}{22}$$
Now solve the equation $x=\frac{-19±\sqrt{537}}{-22}$ when $±$ is minus. Subtract $\sqrt{537}$ from $-19$.
$$x=\frac{-\sqrt{537}-19}{-22}$$
Divide $-19-\sqrt{537}$ by $-22$.
$$x=\frac{\sqrt{537}+19}{22}$$
Factor the original expression using $ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right)$. Substitute $\frac{19-\sqrt{537}}{22}$ for $x_{1}$ and $\frac{19+\sqrt{537}}{22}$ for $x_{2}$.
