Solve $LaTeX: \displaystyle 12 x^{2} + x - 6=0$

This is an ac method factoring. The factors of $LaTeX: \displaystyle ac = -72$ that add up to $LaTeX: \displaystyle 1$ are $LaTeX: \displaystyle -8$ and $LaTeX: \displaystyle 9$ . Separating gives $LaTeX: \displaystyle (12 x^{2} - 8 x)+(9 x - 6)=0$ . This gives $LaTeX: \displaystyle (4 x + 3)(3 x - 2)=0$ . The solutions are $LaTeX: \displaystyle x = - \frac{3}{4}$ and $LaTeX: \displaystyle x = \frac{2}{3}$