It takes time. I'm not sure about the nature of p90 workout but tbh, if you can't get rid of carbs, it's hard to keep up with this diet.
You need to force your body to be in keto stage to reap the full benefits. Caloric deficit is not exactly a way to go (Think if your body is not in keto and is lacking in calories, where does it take from first? Surely not the Body Fats, also if glycogen store is out, where would they attack?)
Also, you're looking into cutting right?
P90X is a HIIT workout. With P90X3, they shortened the duration of the workout to be exactly 30mins. Highly recommended for those with minimal motivation to hit the gym as this can done at home with minimal equipment. They incorporated various workouts like mix martial arts, yoga, pilate, upper body, lower body etc on different days so there is sufficient rest period for the different muscle group and most importantly, a wide variety of interesting exercises that targets the whole body(writing this down also serves to motivate me to complete the 90 days workout - I am 2/3 of the way there
)
I basically cut out everything that contains carb(with the exception of vegetables), that is sweet etc. I limit my fruits intake(raspberries, blackberries, cranberries, lemon and lime) as well as my greek yogurt intake. I don't use sweetener even though most primal/paleo/lchf approve of its usage(sparingly) I never do the urine or blood keto test but I am pretty strict with my diet. I will be damn sad if my body is still not in keto lol.
My main aim with this diet is to reduce my weight till satisfactory, then slowly re-introduce carbs back into my diet to maintain.
Only problem for now is my fats intake