2×81^x+1 - 36^x+1 - 3×16^x+1 = 0

$2 \cdot 81^{x + 1} - 36^{x + 1} - 3 \cdot 16^{x + 1} = 0 \\ \\ 2 \cdot 9^{2(x + 1)} - 9 ^{x + 1} \cdot 4^{x + 1} - 3 \cdot 4^{2(x + 1)} = 0 \ \ \ \ |:4^{2(x + 4) }\\ \\ 2 \cdot (\dfrac{9}{4} )^{2(x + 1)}- (\dfrac{9}{4} )^{x + 1} - 3 = 0 \\ \\ t = (\dfrac{9}{4} )^{x + 1}, \ t \ \textgreater \ 0 \\ \\ 2t^2 - t - 3 = 0 \\ \\ D = 1 + 3 \cdot 4 \cdot 2 = 25 = 5^2 \\ \\ t_1 = \dfrac{1 + 5}{4} = \dfrac{3}{2}\\ \\ t_2 = \dfrac{1 - 5}{4}= -4 - ne \ ed.$

Обратная замена:
$(\dfrac{9}{4} )^{x + 1} = \dfrac{3}{2} \\ \\ (\dfrac{3}{2} )^{2x + 2} = ( \dfrac{3}{2} )^{1} \\ \\ 2x + 2 = 1 \\ \\ 2x = 1 - 2 \\ \\ x = -0,5$