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$$3^{x^2+2x}-3^{x^2+1}-9^{x+1}+27=0$$


$$3^{x^2}(3^{2x}-3) - 3^2(3^{2x}-3)=0$$


$$(3^{x^2}-3^2)(3^{2x}-3)=0$$


$$x = \pm \sqrt{2}, \frac{1}{2} $$