Solve for r:
1/(r^3 + 7) - 7 = -r^3/(r^3 + 7)
Multiply both sides by r^3 + 7:
1 - 7 (r^3 + 7) = -r^3
Expand out terms of the left hand side:
-7 r^3 - 48 = -r^3
Add r^3 + 48 to both sides:
-6 r^3 = 48
Divide both sides by -6:
r^3 = -8
Taking cube roots gives 2 (-1)^(1/3) times the third roots of unity:
r = -2 or r = 2 (-1)^(1/3) or r = -2 (-1)^(2/3)
