You may want to review quadratic equations first.

To solve a quadratic inequality, you get everything on the left-hand side, so the right-hand side is just 0. Try to make it so the leading coefficient is positive (you might have to rewrite the inequality, or multiply both sides by −1). Now there are three cases. If the discriminant is negative, then the side with the variables is always positive, so the solution is either all real numbers or nothing, depending on which way the inequality goes. If the discriminant is positive, then the equation (if we pretend the inequality is an equals sign for a moment) has two real solutions. For example, if the left-hand side were x2 − 8x + 15, the solutions would be 3 and 5. Now you just have to learn the rules. If it's a less-than sign, the answer is (3, 5). If it's a less-than-or-equal sign, the answer is [3, 5]. If it's a greater-than sign, the answer is (−∞, 3) ∪ (5, ∞). Finally, if it's a greater-than-or-equal sign, the answer is (−∞, 3] ∪ [5, ∞).

That covers two cases. The third is trickier. Suppose the discriminant is 0. Then the equation would have one real solution. For example, if the left-hand side were x2 + 2x + 1, the solution would be −1. Then if it's a less-than sign, there's no solution. If it's a less-than-or-equal sign, the answer is just −1. (You can write this as an interval like this: [−1, −1].) If it's a greater-than sign, the answer is all numbers except for −1, so you write (−∞, −1) ∪ (−1, ∞). Finally, if it's a greater-than-or-equal sign, the answer is all real numbers.