Truth be told, there are a few factors:
- The 4mm eyepiece that comes with the Powerseeker just isn't very good, unfortunately.
- Neither is the Barlow that comes with the Powerseeker. This is a serious issue by itself - all Barlows degrade the quality of an image somewhat, even very expensive ones. But the one that comes with the Powerseeker is not fantastic.
- The 4mm is going to give you a magnification of 250x, which is already quite high for being able to control the Powerseeker on its mount, or see through it given its design. Blurry pictures are an extremely common report for this model.
- Problems with the focuser are also somewhat notorious for the Powerseeker series, and it would be unusual in my experience for this to be fixable at-home.
And, as Kavin Ishwaran says - Barlowing 3x up to 750x power is almost certainly going to cause you to see almost nothing. I would not generally dare push that high on a much larger, much more stable telescope. A rule of thumb is that atmospheric conditions will limit your seeing to 400x on an extremely good night - and even on good nights, I try not to push views that hard unless I can seriously justify why I'm trying to do so. So, I'm not shocked you're having trouble with it - it isn't normally possible to get good views with that power at all!
Here are my recommendations:
- Overall, if you are having trouble getting the image to come into sharp focus during the course of normal usage, I'd pack the scope up and return it as defective. (Note: "normal usage" does not include Barlowing the 4mm!) A few people I know have tried their best to correct the focusers on these telescopes via shimming, and despite their skill at telescope making, have had limited success actually improving it due to the design of the telescope.
- Avoid using the Barlow that came with the Powerseeker. More generally, I would recommend avoiding using a Barlow at all at this point, unless you have a very particular reason for doing so. While it might seem like an attractive option, most hobbyists only use 2 or 3 eyepieces almost all of the time, and a Barlow is really a speciality piece of equipment. If you want a specific power, you'll be much happier with a dedicated eyepiece for that power, unless you have a special need for one (generally only if you'd need a very short focal length eyepiece).
- Similarly to the above, if you do continue using the Powerseeker, I'd recommend backing off the 4mm eyepiece - Goldlines, such as the 6mm version, are perfectly good eyepieces, doubly so for the cost.
Overall, bluriness and unsteadiness are, unfortunately, among several highly common frustrations with the Powerseeker 127EQ series that do not appear in other telescopes in the price range. They are a consequence of the construction of the telescope - the way its optics are designed to work, the way it is mounted, and the overall build quality.
I know this isn't advice everyone wants to hear, but if you have the funds available, you may enjoy a different telescope more - for example, a Z100 will have better control, better optics, a more stable mount & base, and will generally allow you a bit more liberty when learning. Check out this guide for more information - really, anything with a Dobsonian design. Or, frankly, a pair of binoculars in the price range of the Powerseeker will do you better as well.