To find the values of a and b, we need to expand the right side of the given equation:

(x + 3)(x + b) = x^2 + bx + 3x + 3b
= x^2 + (b + 3)x + 3b.

Now, we can compare this with the given equation x^2 - ax - 21:

Comparing the x terms:
(b + 3)x = -ax
=> b + 3 = -a
=> a = -b - 3

Comparing the constant terms:
3b = -21
=> b = -7

Substitute the value of b back into the equation for a:
a = -(-7) - 3
a = 7 - 3
a = 4

Therefore, the values of a and b are a = 4 and b = -7.