Let's simplify the given equation step by step:

Let's denote x^2 + 2 as a variable, let's say u. So, the equation becomes $u$^2 - 5u - 6 = 0.

Now, we can factor the quadratic equation $u$^2 - 5u - 6 = 0. The factors are $u-6$$u+1$ = 0.

So, the possible values for u are u = 6 and u = -1.

Substituting back u = x^2 + 2, we get two possible equations:

For u = 6: x^2 + 2 = 6 -> x^2 = 4 -> x = ±2

For u = -1: x^2 + 2 = -1 -> This has no real solutions as x^2 + 2 cannot be negative.

Therefore, the solutions to the given equation are x = 2 and x = -2.