Question

how to solve (a-3)*(a+6)<0

Answer 1

there are two ways the product X*Y can be less than zero.
1. X less than zero Y greater than zero.
2. X greater than zero Y less than zero.
so in this case,
$(a - 3) < 0 \\ (a + 6) > 0 \\ or \\ (a - 3) > 0 \\ (a + 6) < 0$
$a < 3 \\ a > - 6 \\ or \\ a > 3 \\ a < - 6$