To solve $ax^{2+bx+c}$ > 0 (or <, >=, <=): (1) Find discriminant D = $b^{2-4ac}$. (2) If D>0, find roots alpha < beta. (3) For a>0: parabola opens upward → positive outside roots, negative between. For a<0: reversed. (4) Include endpoints for >= or <=. (5) If D=0: expression touches x-axis at one point, sign doesn't change except at that point. (6) If D<0: sign is same as 'a' everywhere. Always sketch the parabola mentally.