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To solve this equation, we can rewrite it as:

6^x - 9(2^x) - 8(3^x) + 72 = 0

Let's make a substitution to simplify the equation. Let's say y = 2^x. Then, we can rewrite the equation as:

(6^x) - 9y - 8(3^(log3(y))) + 72 = 0

Now, let's rewrite the equation in terms of y:

y^3 - 9y - 8 + 72 = 0 y^3 - 9y + 64 = 0

Now, we have a cubic equation in terms of y. We can solve this equation using methods such as factoring, synthetic division, or numerical methods. Once we find the values of y, we can substitute back to find the values of x.