Решите неравенство: (3x+1)(x-2)<6.

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

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

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

\[D = 25 + 96 = 121\]

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

\[x^{2} = \frac{5 - 11}{6} = - 1.\]

\[(x + 1)\left( x - 2\frac{2}{3} \right) < 0\]

\[- 1 < x < 2\frac{2}{3}.\]

\[Ответ:\ - 1 < x < 2\frac{2}{3}.\]