I sell horse equipment and my photos are created against a white background with the items on hooks right against the wall or background. I get a lot of shadows, but it is the only way to display the products. I would love to blow out the background but there is no space between the product and the background.
A two (2) light set up will do this deed. You can use pin-up lamps from the hardware store, best is reflector flood bulbs. Place one lamp high to simulate afternoon sun. Measure distance lamp to subject. Place second lamp at lens height as close to the camera as you can get without it getting in the way. Close placement is the key, you are filling shadows from the camera's viewpoint. Set the second lamp at the same distance as the main light. Shoot a test shot. Back the fill by multiplying its distance by 1.4 and make a test shot. The density of the shadows are thus adjusted by the distance fill lamp to subject.
So MAKE space between sample and background. Hooks don't have to be on walls, they can be on other types of support.
Maybe use black supports and photograph against black. This can be very effective with the right lighting. And 'the right lighting' only needs to be a few cheap LED torches these days.
See how I approached photographing this trinket? A bit smaller than your stuff, yes! But the same idea could work. Total cost of lighting equipment well under £20.
If it must be a white background, be prepared to do some retouching in Photoshop or similar! I very much doubt these pictures came straight from the camera...
Shine (separate) light on the background, not just the objects. If you use flash, this is even more important, or you get hard-edged shadows.
Bounce each light off large, very large white boards placed equidistant on both sides of the camera. Those large surfaces will spread the light evenly across your subject. You may have to boost contrast a bit but your shadow problem will be gone. The reason why you have shadows is because your light source is too small. The larger the source, the softer an more omni-directional the light is. Bounce the light.
Light the background with 2 lights one from each side behind the object. Have another to light the object. Make sure that the ones pointing at the background are brighter than the front light.
An object illuminated by a single light source can produce shadows whose illumination is many f-stops below that of the non-shadowed background. Illuminating the background with even a moderate amount of light can make shadows far less harsh. For example, illumination with 1/3 of the primary light can reduce shadows from being many F-stops to being two. Blowing out the background is seldom necessary nor desirable when trying to create an aesthetically-pleasing shot.
If one wants to completely eliminate the background, one approach is to take one picture with only the background lit, so the entire subject will be dark, and then take another picture with the camera in exactly the same place, focusing only on the illumination of the subject (not worrying about which parts of the background are or are not lit). Once this is done, the two pictures can be composited, with the second one being used to fill in areas that were black in the first. Alternatively, the subject picture can be composited with an separate background picture, using the picture of the lit background as a mask to control which parts of the picture to replace with the new background.
You could just use a translucent background with another light source pointed at from behind.
And of course, you can always just do it the way most websites like The Gap, or Amazon does it, which is to use the pen tool in Photoshop to cut the image out then paste it back on top of a white background.
Lighting is difficult and I am still learning all the tricks. I believe the typical setup for photographing what I am assuming is tack would be a two-light system using two soft-boxes as big as the object being photographed. One soft-box would go on either side of the object at about a 30 degree angle parallel to the wall. You will likely still get some shadows, but the soft-boxes will diminish them - and moving the boxes farther away will diminish them further. I tried to duplicate a setup with the equipment I have - unfortunately I have only one soft box and a gray wall.
I placed a soft box on the right and a reflector umbrella on the left. Here is the result:
You can still see shadows mostly to the right of the "tack" that are generated from the reflector dish, but they are not as distracting as they would be with direct lighting.
If you don't have or want to invest in this kind of equipment, you might be able to get the same result using large work lights and some kind of material in front of them to diffuse the light.
The alternative - depending on where your wall is located - is to not use any direct lighting. If there is enough indirect lighting from doors, windows, overhead lights, etc., you can take a photo with virtually no shadows by adjusting your camera settings to take advantage of the natural light.
Here is my shop, where I had my "tack" wall set up.
Light hits the "wall" from the garage door in the back, the windows on each side and the overhead florescent lights. A photo of this arrangement came out with very few shadows.
The photo was shot at about 6:00 PM with an f-stop of 5.6, a 1/30 exposure time and an ISO of 400. The drawback with this approach is that the color doesn't pop as much in low light. If you are experienced with post-processing tools, you can make some good improvements to this photo, but it may look bland otherwise. (I did a little post-processing on this shot to show what is possible.)
And if by chance the white wall you are using has adjoining white walls and ceilings, you might try pointing work lights at the walls and ceiling and use the diffused reflection to light the object of interest. The bounced light should have few if any shadows.
Minature LED lights will do the trick. Put them inside clothes and under shoes and even the floor!