Solve $LaTeX: \displaystyle 6 x^{2} - 5 x - 25=0$

This is an ac method factoring. The factors of $LaTeX: \displaystyle ac = -150$ that add up to $LaTeX: \displaystyle -5$ are $LaTeX: \displaystyle -15$ and $LaTeX: \displaystyle 10$ . Separating gives $LaTeX: \displaystyle (6 x^{2} - 15 x)+(10 x - 25)=0$ . This gives $LaTeX: \displaystyle (3 x + 5)(2 x - 5)=0$ . The solutions are $LaTeX: \displaystyle x = - \frac{5}{3}$ and $LaTeX: \displaystyle x = \frac{5}{2}$