Solve $LaTeX: \displaystyle 10 x^{2} - 3 x - 18=0$

This is an ac method factoring. The factors of $LaTeX: \displaystyle ac = -180$ that add up to $LaTeX: \displaystyle -3$ are $LaTeX: \displaystyle -15$ and $LaTeX: \displaystyle 12$ . Separating gives $LaTeX: \displaystyle (10 x^{2} - 15 x)+(12 x - 18)=0$ . This gives $LaTeX: \displaystyle (5 x + 6)(2 x - 3)=0$ . The solutions are $LaTeX: \displaystyle x = - \frac{6}{5}$ and $LaTeX: \displaystyle x = \frac{3}{2}$