Factor x and constant terms from the left hand side: -x (n - x^8) = 0
Multiply both sides by -1: x (n - x^8) = 0
Split into two equations: x = 0 or n - x^8 = 0
Subtract n from both sides: x = 0 or -x^8 = -n
Multiply both sides by -1: x = 0 or x^8 = n
Taking 8^th roots gives n^(1/8) times the 8^th roots of unity: Answer: x = 0 or x = -n^(1/8) or x = -i n^(1/8) or x = i n^(1/8) or x = n^(1/8) or x = -(-1)^(1/4) n^(1/8) or x = (-1)^(1/4) n^(1/8) or x = -(-1)^(3/4) n^(1/8) or x = (-1)^(3/4) n^(1/8)
