To solve this equation, we first need to simplify it:

(1/5)^21 - 2x = 25^3x + 7

We can rewrite (1/5)^21 as 5^(-21):

5^(-21) - 2x = 25^3x + 7

Next, we can simplify 25^3x as (5^2)^3x = 5^6x:

5^(-21) - 2x = 5^6x + 7

Now we need to get the bases of the exponents to be the same:

5^(-21) = 5^6x

By setting the exponents equal to each other:

-21 = 6x

Now, divide both sides by 6 to solve for x:

-21 / 6 = x
x = -3.5

Therefore, the solution to the equation is x = -3.5.