Best way to remove background & keep every hair

Yes it takes time to get use to layers and blending then with different modes and refining mask. Often users will use the quick selection tool and refine the edges then get frustrated because they loose some hair. In the case like your they don't realize that they have actually created the perfect mask inverted. Simply load the mask as a selection then use inverse. Add a replacement background layer over the image the add a layer mask with the selection active. I did that with your image. Added a 50% gray layer I texurized made blending mode overlay then added a hue/saturation colorize adjustment layer so I could make the gray any color.

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Here is a reduced size animated Gif click on it to see the animation

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JJMack