How to use algebra to solve this?

Question

Use Algebra to solve for $x$: $8(9^x)+3(6^x)-81(4^x)=0$

My attempt was to decompose the exponential functions into $2^x$ and $3^x$ where possible and then substitute them for some $p$ and $q$. I was stuck after this though. Also, are there any more general techniques for solving equations where exponential functions are present?

Answer 1

$$8q^2+3qp-81p^2=0$$ factors as

$$(q-3p)(8q+27p)=0.$$

Hence

$$\left(\frac 32\right)^x=3.$$

The right factor yields no real root.