When adjusting the handles of an anchor point, how can I adjust both handles to an equal length or adjust them both at the same time?
As @llan answered, you can use the Convert Anchor Tool to click-drag two symmetrical handles out from an anchor point.
If you already have two non-symmetrical handles, or just one handle and want a second one, Illustrator provides no method to easily match two (or more) non-symmetrical handles other than this click-drag option of the Convert Anchor Tool.
In other words, no. You can't really alter two handles simultaneously unless they are smooth point handles.
If you want the handles to be "similar" the first thing you do - you press Shift+C (Convert Anchor Point) and click once on the point of interest: you had a smooth point (otherwise it has no handles) and converted it to sharp one.
Next, you click on the point of interest the second time and begin to drag to desired direction - by this action you convert the point to smooth and operate its handles at the same time and the same degree.
If you select the anchor point (A) and hit S to scale, it proportionally scales the lengths of each handle. To get equal length handles from an existing uneven point, the only way I know of is to convert it to a non-handled point, maybe marking the goal handle endpoint with a line (leave the anchor point selected, then use \ to make a little line), then re-drag handles off of the point.