Найдите множество решений неравенства: (3x+1)(x-2)<6.

\[(3x + 1)(x - 2) < 6\]

\[3x^{2} - 6x + x - 2 - 6 < 0\]

\[3x^{2} - 5x - 8 < 0\]

\[3x^{2} - 5x - 8 = 0\]

\[D = 25 + 96 = 121\]

\[x_{1} = \frac{5 + 11}{6} = 2\frac{2}{3}\]

\[x_{2} = \frac{5 - 11}{6} = - 1\]

\[Ответ:x \in \left( - 1;2\frac{2}{3} \right)\text{.\ }\]