Solve $LaTeX: \displaystyle - 3 x^{2} - 57 x - 270=0$

Since the GCF is $LaTeX: \displaystyle -3$ we need we factor out the GCF to get $LaTeX: \displaystyle -3(x^{2} + 19 x + 90)$ . This is now a pq method factoring. The factors of $LaTeX: \displaystyle 90$ that add up to $LaTeX: \displaystyle 19$ are $LaTeX: \displaystyle 10$ and $LaTeX: \displaystyle 9$ . This gives $LaTeX: \displaystyle -3(x + 10)(x + 9)=0$ . The solutions are $LaTeX: \displaystyle x = -10$ and $LaTeX: \displaystyle x = -9$