you have to submit plans to put up a three sided small fence for it??

just put up some small trellis things and put some potted plants around it

there are tons of ideas. just google, "how to hide AC unit in yard"

Thanks, I’ve seen these everywhere but it doesn’t address the utilities on the back of the building. Just hoping for some imaginative suggestions. The bushes might work but I’m not sure how to keep the root system clear of all the underground cables and wires (marked in colors).

I’ve heard about painting the utility boxes to match the house they don’t stand out as much?

These are moveable so the hoa shouldnt object and if you grow vines they don’t need deep roots,but protect them well if You live in a wintry area, or plant fast growing annuals each year

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You can also use hanging baskets on then, or fill with potted plants and climbing vinres rather than fill the box with soil

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This style might go best with your area

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Don't worry about covering the utility stuff, just make your patio private. Making the patio larger and installing a fence with planter and/or seating might be worth doing the survey, etc., your HOA requires.

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There are all kinds of ideas to create a visual barrier and consider what would also be a bonus for patio usage.