This subsection is not completed yet, but in the meantime here are some practice questions.
When solving a quadratic inequality, it helps to graph the parabola. For example, if \[(x-2)(x+3) \gt 0\] then draw a graph of $(x-2)(x+3)$: The graph doesn’t need to be detailed; just show the $x$-intercepts and get the parabola facing the correct way depending on the $x^2$ coefficient. Then it’s clear that our solution is $x\lt -3,\, x\gt 2$. If the parabola was facing the other way, or the inequality was actually $(x-2)(x+3) \lt 0$ then the solution would be $-3\lt x\lt 2$.