( x + 4)^3 + (x + 5)^3 = (x + 7)^3 + ( x - 4)^3
In the expansion of this, the x^3 terms on each side will "cancel" and we are left with
3x^2(4) + 3x(4)^2 + 4^3 + 3x^2(5) + 3x*(5)^2 + 5^3 = 3x^2(7) + 3x(7)^2 + 7^3 - 3x^2(4) + 3x(4)^2 - 4^3
Simplify
12x^2 + 48x + 64 + 15x^2 + 75x +125 = 21x^2 + 147x + 343 - 12x^2 + 48x - 64
27x^2 + 123x + 189 = 9x^2 + 195x + 279
18x^2 - 72x - 90 = 0 divide through by 18
x^2 - 4x - 5 = 0 factor
(x - 5) ( x + 1) = 0
Set each factor to 0 and solve for x and we get that
x = 5 or x = -1