solve quadiratic inequalitiy using product propertise

Question

6xsq -x+3<5xsq+5x-5

Answer 1

If you mean

6x^2-x+3 < 5x^2+5x-5

then just collect terms on one side, and you get

x^2-6x+8 < 0
(x-2)(x-4) < 0

This is a parabola which opens upward, so it is negative between the roots. Thus
2 < x < 4

A product is negative if exactly one of the factors is negative.