To solve for p, we have to put the equation in the specific format that is required, which is (x+p)^2 = q.
For this equation, we start off with the equation given, which is x^2 - 6x = 12.
The equation x^2 - 6x = 12 can be rewritten in the form (x+p)^2 = q, which is obtained by completing the square.
Completing the square involves taking the coefficient of the x term (which is -6), dividing it by 2, and then squaring it. Applied to our problem, the coefficient -6 divided by 2 equals -3, and squaring -3 gives us the 9.
So, by adding 9 in both side of the equation which doing to keep the equation balance, we get the following equation: x^2 - 6x + 9 = 12 + 9.
This can be rewritten as (x-3)^2 = 21. So in comparison with the format ((x+p)^2 = q), it's clear that p equals -3.
Therefore, the value of p, given the equation can be rewritten as (x+p)^2 = q, is -3.