Solve $LaTeX: \displaystyle - 3 x^{2} - 9 x + 12=0$

Since the GCF is $LaTeX: \displaystyle -3$ we need we factor out the GCF to get $LaTeX: \displaystyle -3(x^{2} + 3 x - 4)$ . This is now a pq method factoring. The factors of $LaTeX: \displaystyle -4$ that add up to $LaTeX: \displaystyle 3$ are $LaTeX: \displaystyle -1$ and $LaTeX: \displaystyle 4$ . This gives $LaTeX: \displaystyle -3(x - 1)(x + 4)=0$ . The solutions are $LaTeX: \displaystyle x = 1$ and $LaTeX: \displaystyle x = -4$