$\begin{array}{l}
 {7^2}\cdot{x^6} + 3\cdot{7^3}\cdot{x^5} + 5\cdot{7^4}\cdot{x^4} + 5\cdot{7^5}\cdot{x^3} + 3\cdot{x^2}\cdot{7^6} + x\cdot{7^7} = 0 \\ 
 {7^2}\cdot x({x^5} + 3\cdot7\cdot{x^4} + 5\cdot{7^2}\cdot{x^3} + 5\cdot{7^3}\cdot{x^2} + 3\cdot{7^4}x\cdot + {7^5}) = 0 \\ 
 {x_1} = 0 \\ 
 {x^5} + 3\cdot7\cdot{x^4} + 5\cdot{7^2}\cdot{x^3} + 5\cdot{7^3}\cdot{x^2} + 3\cdot{7^4}x\cdot + {7^5} = 0 \\ 
 (x + 7){({x^2} + 7x + {7^2})^2} = 0 \\ 
 {x_2} =  - 7 \\ 
 {x^2} + 7x + {7^2} = 0 \\ 
 ... \\ 
 \end{array}$