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 $ax^{2}+bx+c=0$.
$$-x^{2}-15x-10=0$$
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 $x=\frac{15±\sqrt{185}}{-2}$ when $±$ is plus. Add $15$ to $\sqrt{185}$.
$$x=\frac{\sqrt{185}+15}{-2}$$
Divide $15+\sqrt{185}$ by $-2$.
$$x=\frac{-\sqrt{185}-15}{2}$$
Now solve the equation $x=\frac{15±\sqrt{185}}{-2}$ when $±$ is minus. Subtract $\sqrt{185}$ from $15$.
$$x=\frac{15-\sqrt{185}}{-2}$$
Divide $15-\sqrt{185}$ by $-2$.
$$x=\frac{\sqrt{185}-15}{2}$$
Factor the original expression using $ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right)$. Substitute $\frac{-15-\sqrt{185}}{2}$ for $x_{1}$ and $\frac{-15+\sqrt{185}}{2}$ for $x_{2}$.
