Question

(x + 3)(x - 5) < 0
=x * x + x * -5 + 3 * x + 3 * -5
= x ^ 2 + 3x - 5x - 15
= x ^ 2 - 2x - 15 < 0
as two of the terms have a minus sign

Answer 1

What are you supposed to do ?
Solve it ? or expand it ?

for expanding your notation form is poor, don't use the "=" sign

correct way:
(x + 3)(x - 5) < 0
x * x + x * -5 + 3 * x + 3 * -5 < 0
x ^ 2 + 3x - 5x - 15 < 0
x ^ 2 - 2x - 15 < 0

If you are solving, consider the parabola
f(x) = (x + 3)(x - 5)
It would cross the x-axis at -3 and 5 and would open upwards, so
-3 < x < 5 is your solution