To solve this equation, we can simplify both sides by combining the exponents of the same bases:

2^(x+1) 5^x = 10^(x+1) 5^(x+2)

2^(x) 2^1 5^x = 10^(x) 10 5^x * 5^2

2^(x) 2 5^x = 10 10^(x) 5^x * 25

2^(x) 2 5^x = 10 10^(x) 5^(x+2)

Now, we can express 10 as a power of 2 and 5:

2^(x) 2 5^x = 2^1 5 2^(x) * 5^(x+2)

2^(x) 2 5^x = 2 5 2^(x) * 5^(x+2)

Now, we can see that the equation holds true for all values of x. Therefore, the solution to the equation is x belongs to all real numbers.