The question is ambiguous but let's start with 10^(x(2x+1))-1000=0.
10^(x(2x+1))=10^3, then x(2x+1)=3, 2x^2+x-3=0, (2x+3)(x-1)=0 so x=1 or -3/2.
Let's now look at (10^x)(2x+1)-1000=0. 2x+1=10^(3-x), the solution of which is x=2.2583 approx. (using an iterative method).