Solve $LaTeX: \displaystyle 2 x^{2} + 38 x + 180=0$

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