I just wanted to add something here... I'm not sure if it's been covered or not, but since I don't see it online much, I just wanted to add that if your laundry detergent separates, all that you need to do is re-cook everything and it'll come out like it's supposed to.

I've also learned that if you recook it and all that good stuff, do NOT use a stick blender once it's cooled, because it'll just cause it to separate again, then you'll have to cook it a third time... Ask me how I know, lol.
As for potassium hydroxide, the whole thing just irritates me. Everyone says that you should only use KoH for liquid soaps, but it's just not true. I've used my NaOH for liquid soaps without issues. MANY people who say to use KOH tell you to add salt later to thicken it up... Why? Why use the more expensive KOH to make soap, then "render" it into a NaOH soap?! Just start out with the NaOH and go from there.