Find all real numbers a that satisfy 1/(a^3 + 7) - 7 = -a^3/(a^3 + 7) + 6.
Rearrange as
a^3 / (a^3 + 7) + 1 / (a^3 + 7) = 13
(a^3 + 1) / (a^3 +7) = 13
a^3 + 1 = 13 (a^3 + 7)
a^3 + 1 = 13a^3 + 91
-12a^3 = 90
a^3 = -90 / 12 = -15/2 take the cube root
a = (-15/2)^(1/3) = - (15/2)^(1/3)
