How to solve this ( and general )logarithmic Equation $$ 4^{x+1} - 6^x - 2*9^{x+1} = 0$$
I recently stumbled across this logarithmic Equation and really I have no clue how to solve this. Also , please provide a tactical way to approach such questions 

Hint:
$$2^{x+1}\times 2^{x+1} -2^x\times 3^x-2\cdot3^{x+1}\times 3^{x+1}=0$$
$$2\cdot 2^x\cdot 2^x\cdot 2-2^x\cdot 3^x-2\cdot 3^x\cdot3\cdot3^x\cdot 3=0$$
$$a:=2^x,\qquad b:=3^x$$
$$4\cdot a^2-a\cdot b-18\cdot b^2=0$$
$$(a+2b)(4a-9b)=0$$
