It's difficult to describe the process in words, so you might do better with studying some online lessons that show pictures of the process.
Once you've learned the basic process, look at the two factors you have. The factors x + 9 and x + 2 split the number line into the intervals (-infinity, -9), (-9, -2), and (-2, +infinity). From what you know of graphing, you already know that the quadratic is above the axis (that is, greater than zero) on its "ends", so you already know which two intervals you need for your solution.
But looking at the signs of the factors, you have x + 9 > 0 for x > -9, and x + 2 > 0 for x > -2. Then the two factors together are positive (that is, the quadratic is positive) where both factors are positive or else both are negative. Both are negative for x < -9 and both are positive for x > -2.