To solve this equation, we need to expand the right side of the equation by multiplying (x+9)(x-a):

(x+9)(x-a)
= x^2 - ax + 9x - 9a
= x^2 + (9-a)x - 9a

Now, we know that this expanded form should be equal to x^2 + 6x - 27:

x^2 + (9-a)x - 9a = x^2 + 6x - 27

Comparing the coefficients of x on both sides, we get:

9 - a = 6

Solving for a, we have:

9 - 6 = a
a = 3

Therefore, the value of a is 3.