Problem with multiplying and dividing algebratic equations

hi, i am able to do the equation though my problem is that i do not know when a number is a positive or negative. for example....
if the equation is (x-3)(4+x) - (x+6)(x-3)
i heard that the second part becomes all negative though it really confuses me....
i get my answer right though when i right the number has a negative, it is actually a positive and it confuses me because i know that negative times a positive is always a negative though it doesnt seem to be like that in this case

i hope i did not confuse you but it is annoying me
thanks

one step at a time:
= (x^2 + x - 12 ) - (x^2 + 3x - 18) => now multiply the negative inside:
= x^2 + x - 12 - x^2 - 3x + 18
= -2x + 6

you are welcome dear.

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remember
positive times a poitive is poistive
negatvie times a negative is positive
positive times a negative is negative

your equation
(x-3)(4+x)-(x+6)(x-3)

You can apply the negative to one of the factors (x+6) or (x-3) but not both at the same time.
your orriginal equation
(x-3)(4+x)-(x+6)(x-3) = (x-3)(4+x)+(-x-6)(x+3) = (x-3)(4+x)+(x+6)(-x+3)

Or you could multiply the factors together
(x²+x-12)-(x²+3x-18) = (x²+x-12)+(-x²-3x+18)
Notice not everything on the right is negative, we just flipped all the signs around
this can be simplified to:
6-2x

Negative multiplied with negative = Positive.
Negative with positive (and vice versa) = Negative.

So, if you wanna solve the second part of the equation, you'll get-
-x(sqaured i.e. raised to the power of 2) +3 + 6x -18