In your example, the Solver found the answer in column B (result = 0) after only 5 iterations, so it stopped. It did not need more. I assume that in column C, Solver did not find a solution but ended after only a few iterations. Since you did not provide the function, or the Solver settings, I'm afraid I don't have much to work with. If it ends so quickly, my best guess is that your function is non-continuous. Some of the Solver methods only work on continuous functions. Try again using each of the different Solving Methods. Evolutionary is probably the one that would work best, but it still strongly depends on your function.

As far as getting a "close" answer instead of an exact one, if an exact one doesn't exist, it depends on your function again. If the result of the function in B66 is always non-negative, you can just change the Solver settings to "minimize the value" instead of setting it to 0. If the function can be negative, wrap it in an ABS function, then choose "minimize the value".

I don't know what your function is, but sometimes it's possible to rewrite it so that it behaves better for Solver, but that's probably up to you.