Solve $LaTeX: \displaystyle - 5 x^{2} + 20 x + 225=0$

Since the GCF is $LaTeX: \displaystyle -5$ we need we factor out the GCF to get $LaTeX: \displaystyle -5(x^{2} - 4 x - 45)$ . This is now a pq method factoring. The factors of $LaTeX: \displaystyle -45$ that add up to $LaTeX: \displaystyle -4$ are $LaTeX: \displaystyle 5$ and $LaTeX: \displaystyle -9$ . This gives $LaTeX: \displaystyle -5(x + 5)(x - 9)=0$ . The solutions are $LaTeX: \displaystyle x = -5$ and $LaTeX: \displaystyle x = 9$