Phương trình đã cho tương đương với:
$2\left(\dfrac{4}{9}\right)^{x^2+1}+\left(\dfrac{2}{3}\right)^{x^2+1}=1$
$\Leftrightarrow \left(\dfrac{2}{3}\right)^{x^2+1}=\dfrac{1}{2}$
$\Leftrightarrow \left(\dfrac{3}{2}\right)^{x^2+1}=2$
$\Leftrightarrow x^2+1=\log_{\frac{3}{2}}2$
$\Leftrightarrow x=\pm\sqrt{\log_{\frac{3}{2}}2-1}$