Dying black hair red?

Hi :)
I've had black hair for about 6months, a few months ago I died the bangs blonde with peroxide. Then I got bored quickly and dyed all my hair back to black with semi-permanent dye. Currently my hairs mostly black, but the bits that were previously blonde have faded to a dark purple.
My hairs still in good condition but I really want to dye it bright red (like the colour the twin have on skins?). How do I go about doing this? Do I need to peroxide my hair first? Will it all go one uniform colour? Can I avoid damaging my hair too much?

Sorry for the information overload, I'm just useless when it comes to hair/beauty and would like to have a rough idea of what to do before I go buy some dye :)