Solve $LaTeX: \displaystyle 2 x^{2} + 32 x + 126=0$

Since the GCF is $LaTeX: \displaystyle 2$ we need we factor out the GCF to get $LaTeX: \displaystyle 2(x^{2} + 16 x + 63)$ . This is now a pq method factoring. The factors of $LaTeX: \displaystyle 63$ that add up to $LaTeX: \displaystyle 16$ are $LaTeX: \displaystyle 7$ and $LaTeX: \displaystyle 9$ . This gives $LaTeX: \displaystyle 2(x + 7)(x + 9)=0$ . The solutions are $LaTeX: \displaystyle x = -7$ and $LaTeX: \displaystyle x = -9$