Is a teacher or textbook actually giving you algebra problems that ask you to solve for i??? And using x as the multiplication operator? The choice of variables /operator symbols is quite bizarre. Nonetheless, while that is important, you probably did not come here to hear that. Here's what's up:

10.5754 x i = 1 -[1/(1+i)^12]

So, we have 10.5754i = 1 - [1/(1+i)^12]

If this is what you mean, then you should get 13 solutions, however, 11 of them will be complex (meaning using of "i"), another should be zero, and the final solution (13th solution) is almost .02. In fact, it is something along the lines of .0199991 per some online calculator I just grabbed. This 0.199991, or simply 0.2 solution is the only real positive solution you get. I this what you were looking for? Are you sure this was how the problem was assigned?

-Andy