7.220. $3^{2 x+4}+45 \cdot 6^{x}-9 \cdot 2^{2 x+2}=0$.

7.220. $3^{2 x+4}+45 \cdot 6^{x}-9 \cdot 2^{2 x+2}=0$. 

(No change needed as the text is already in English and contains only a mathematical equation.)
Solution.

Rewrite the equation as $81 \cdot 3^{2 x}+45 \cdot 3^{x} \cdot 2^{x}-36 \cdot 2^{x}=0$. Dividing it by $9 \cdot 2^{2 x}$, we get $9 \cdot\left(\frac{3}{2}\right)^{2 x}+5 \cdot\left(\frac{3}{2}\right)^{x}-4=0 \Rightarrow\left(\frac{3}{2}\right)^{x}=-1$ (no solutions), or $\left(\frac{3}{2}\right)^{x}=\left(\frac{3}{2}\right)^{-2}$, from which $x=-2$.

Answer: -2 .