You have a LOT of research to do before even moistening those seeds.

You need to look up the proper germination technique, soil for the 3 main stages of growth, lighting type for the 3 stages of growth, and nutrients.

No, do not put seeds under a HPS, it is not the best way. Small plants want light in the blue spectrum and not a lot of heat. Tomato food is not right either. Seedlings should not be fed until they have 4-5 sets of TRUE adult leaves.

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