<s>[INST] Find solution set of $\dfrac{8^x+27^x}{12^x+18^x}=\dfrac{14}{12}$ What I've done is factoring it.
$$\dfrac{2^{3x}+3^{3x}}{2^{2x}\cdot 3^{x}+3^{2x}\cdot{2^{x}}}=\dfrac{7}{2\cdot 3}$$
This looks like it can be factored more but it doesn't work from my attempts.
 [/INST] Rearrange the equation 
$$6(8^x+27^x)-7(12^x+18^x)=0$$
and factorize 
$$(2^x+3^x)(3\cdot 3^x - 2\cdot 2^x)(2\cdot 3^x - 3\cdot 2^x)=0
$$ 
which leads to the solutions $x=\pm1$.
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