To solve this equation, let's make a substitution to simplify the expression. Let's substitute u = x^2 - 9.

So, the equation becomes: u^2 - 8u + 7 = 0.

Now, we can factor this quadratic equation:

(u - 7)(u - 1) = 0

Setting each factor equal to zero gives us:

u - 7 = 0 or u - 1 = 0
u = 7 or u = 1

Now, substitute back x^2 - 9 for u:

x^2 - 9 = 7 or x^2 - 9 = 1

x^2 = 16 or x^2 = 10

Taking the square root of both sides gives us two possible solutions for x:

x = ±4 or x = ±√10

Therefore, the solutions to the given equation are:
x = 4
x = -4
x = √10
x = -√10