9^{1-(x+2)^2}-2*3^{2-(x+2)^2}+7=0\\ \frac{9}{9^{(x+2)^2}}-\frac{2*9}{3^{(x+2)^2}}+7=0\\ 3^{(x+2)^2}=t\\ \frac{9}{t^2}-\frac{18}{t}+7=0\\ t^2 \neq 0; t \neq 0;\\\\ 9t-18t^2+7t^3=0\\ t(9-18t+7t^2)=0\\ t=0\\ 9-18t+7t^2=0\\ D=324-4*7*(-9)=576\\ t_{2,3}=\frac{18\pm 24}{14}=3;-\frac{3}{7}\\ \\ 3^{(x+2)^2}=3\\ (x+2)^2=1\\ x^2+4x+4=1\\ x^2+4x+3=0\\ D=16-4*1*3=4\\ x_{1,2}=\frac{-4\pm 2}{2}=-1;-3\\ 3^{(x+2)^2}\ \neq-\frac{3}{7}