To solve this equation, we can rewrite it in terms of a common base. Let's rewrite the equation with a base of 3:

$$
3^{2x} - 3^{2(x+1)} - 3^{x+2} + 36 = 0
$$

Now we can simplify the equation:

$$
9^x - 9(9^x) - 3(3^x) + 36 = 0
$$

Let's substitute (9^x = y) to simplify the equation further:

$$
y - 9y - 3\sqrt{y} + 36 = 0
$$

This is a quadratic equation in terms of (y). Let's rearrange the equation:

$$
-8y - 3\sqrt{y} + 36 = 0
$$

Now, let's substitute back (y = 9^x):

$$
-8(9^x) - 3\sqrt{9^x} + 36 = 0
$$

From here, we can solve for (9^x), and then solve for (x) by taking the logarithm of both sides. The solution will likely involve the use of numerical methods like Newton's method due to the complexity of the equation.