Verified answer

5^2x - 7^x -35*5^2x + 35*7^x=0,

5^2x - 7^x -35(5^2x - 7^x)=0,

-34(5^2x - 7^x)=0,

(5^2)^x - 7^x=0,

(25/7)^x=1,

x=0