Они были заинтересованы в том, чтоб

Они были заинтересованы в том, чтобы книгу опубликовали как можно быстрее

Результаты (английский) 1:

They were interested in having a book published as quickly as possible

Результаты (английский) 2:

They were interested in the fact that the book published as soon as possible

Результаты (английский) 3:

they were interested in getting the book published as soon as possible.