Complex sentence: The LDS Church was organized under the leadership of Smith in Fayette, New York, on April 6,1830, soon after Smith's translation of the Book of Mormon from which adherents--also called Latter-day Saints--get their nickname "Mormons".
Split into simpler sentences: The LDS Church traces its history to Joseph Smith from Fayette, New York, on April 6,1830. Soon after Smith's translation of the Book of Mormon, adherents were nicknamed "Mormons".