7.073. $9^{x^{2}-1}-36 \cdot 3^{x^{2}-3}+3=0$.
Solution.

We have $\frac{9^{x^{2}}}{9}-36 \cdot \frac{3^{x^{2}}}{27}+3=0, \quad 3^{2 x^{2}}-12 \cdot 3^{x^{2}}+27=0$. Solving this
equation as a quadratic in terms of $3^{x^{2}}$, we get $3^{x^{2}}=3$, from which $x^{2}=1, x_{1,2}= \pm 1$, or $3^{x^{2}}=9$, from which $x^{2}=2, x_{3,4}= \pm \sqrt{2}$.

Answer: $-\sqrt{2} ;-1 ; 1 ; \sqrt{2}$.