# How do you solve (3x +1)(5 - 10x) > 0?

$\left(3 x + 1\right) \left(5 - 10 x\right) = - 30 {x}^{2} + 5 x + 5$
is an inverted parabola, cutting the $x$ axis at the two points at which its value is zero, that is $x = - \frac{1}{3}$ and $x = \frac{1}{2}$
As $x \to - \infty$ or $x \to \infty$, the $- 30 {x}^{2}$ becomes dominant, and the quadratic has a negative value. So the region in which it has a positive value is $- \frac{1}{3} < x < \frac{1}{2}$