integer values for x such that the equation is a prime number

This is my best attempt :

l 4x^2 - 12x -27 l    can be factored as 

l (2x - 9) (2x + 3 ) l   =

l 2x - 9 l  *  l 2x + 3 l

To be prime either the first factor must possibly be 1  or -1    or the same for the second factor

So

2x - 9 = 1      means that x = 5       and 2(5)+ 3 = 13....so  this value for x generates a prime

2x - 9 = - 1   means that x  = 4      and 2(4) + 3 = 11.....so this value for x geherates a prime

Also

2x + 3 = 1    means that x = -1    and 2(-1) - 9 = - 7  ...but l -7l = 7....so this value for x generates a prime

2x + 3 = -1   means that x =  -2    and 2(-2) - 9 = -5  ...but l -5 l = 5...so this value for x generates a prime

So I find four integer values for x ⇒  { -2, -1, 4 , 5 }