How do I list all the rational zeros for a polynomial function

The polynomial is f(x) = x^6-2x^4-11x^2+12

I need to list all the possible rational zeros.
I don't even know how to start this. Step-by-step process, anyone? I'm desperate.

x^6 - 2x^4 - 11x^2 + 12
= x^6+ 0x^5 - 2x^4 + 0x^3 - 11x^2 + 0x + 12

sum of coefficients
1 – 2 – 11 + 12 = 0
so (x – 1) is a factor
find other fraction by long division or synthetic division
1 | 1 + 0 – 2 + 0 – 11 + 0 + 12
------- + 1 + 1 – 1 – 1 – 12 – 12
--------------------------------------…
---- 1 + 1 – 1 – 1 – 12 – 12 + 0
other factor is
x^5 + x^4 – x^3 – x^2 – 12x – 12
try (x + 1) is a factor or not
(–1)^5 + (–1)^4 – (–1)^3 – (–1)^2 – 12(–1) – 12
= – 1 + 1 + 1 – 1 + 12 – 12 = 0
so (x + 1) is a factor
other factor by synthetic division
– 1 | 1 + 1 – 1 – 1 – 12 – 12
---------- – 1 + 0 + 1 + 0 + 12
--------------------------------------…
----- 1 + 0 – 1 + 0 – 12 + 0
other factor is
x^4 – x^2 – 12
= (x^2 – 4)(x^2 + 3)
= (x + 2)(x – 2)(x² + 3)
= (x + 1)(x – 1)(x + 2)(x – 2)(x² + 3)
----

Factor it (probably by grouping) so you end up with something that looks like f(x)=(x+number)(x+number)
Or minus a number, doesn't matter :p
Then think, what does x have to be in order for each bracket to equal 0? Will be 2 answers (one for each bracket).

EXAMPLE:
Let's say you have (x-6)(x+15)
For the first bracket, x cannot be 6, because 6-6=0. Now for the second bracket, x can not be -15, as (-15)+15=0.
For the final answer you put

X cannot be 6, -15
And for the 'cannot be' part, put an equal sign with a / through it to indigate "can't be equal to"