Here’s the basics for stretching a square/ rectangle room. I’d make the fireplace wall the step 5 wall. Don’t cut out the hearth until you are actually doing step 5. Make sure the carpet is rubbed down on the pins real good before you stretch away from the hearth.
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CJ said, stretch away from the hearth. Good advice.
So I'd stretch across the hearth to the left and then I'd stretch it to the right and then I'd.....
....do the hokey pokey and...
Okay seriously. You need a stretcher that has poles that will telescope from one wall across the room to the other wall. I looked at the harbor freight unit that looks like it may be good for 6 or 8 ft? That's not enough.
I would start on the left hand side and stretch parallel to the fireplace to the right side for 3 ft or so.
Next, I would turn my stretcher around and stretch the opposite direction and stretch it onto the tackstrip pins for about 3 feet.
You'd know almost immediately if its possible to get all those wrinkles out. If not, you can come very close.
My next stretch would be very tricky but I do that type of thing fairly often.
I carry around fairly often, a 4x4, 8 to 12 ft long. I will lay it across the face of a fireplace but I will support it on each side of the fireplace with a couple of 32 inch 4x4s. It forms a bit of a u-shape and forms a wall out around the fireplace for you to stretch off of. In your situation a cheater device called a stinger would probably work for that purpose.
Once I stretched to the middle of the room, directly away from the fireplace, I might rearrange my stretcher tubes and stretch left of the fireplace, then to the right of the fireplace, in equal amounts.
After that I'd stretch straight away from the fireplace to the left and then to the right.
The sequence and the purpose would be much more understandable to a carpet installer, mainly as to what you're trying to achieve. You are trying to stress the carpet equally in all directions.
It's extremely obvious that the fellow that installed this carpet originally did the hokey pokey. He didn't own a stretch her and I'm not sure if he even used his kicker. It's ridiculous to have that many wrinkles at the face of a fireplace. The cabinet installer was a carpet hack. I do think that his crappy work can be fixed one of those wrinkles can be removed.
A lot of the problems that we see in our comments might change because we can't see the opposite side of the room.
What is opposite of the fireplace, doorways, doorways with carpet seams?
The left and right stretch is to remove the wrinkles of the easy part but we don't know what happens when we move those wrinkles and into the right and the inch to the left and what the stretching might affect.
A couple more pictures might help showing what's on the opposite side of the room from the fireplace.
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