To solve the equation, we need to isolate the variable x.

First, let's simplify the equation by cubing both sides:

(x - 3)^3 = 4^3

(x - 3)(x - 3)(x - 3) = 64

Now, let's expand the left side of the equation:

(x^2 - 6x + 9)(x - 3) = 64

x^3 - 9x^2 + 27x - 9x^2 + 54x - 162 = 64

x^3 - 18x^2 + 81x - 162 = 64

Next, let's combine like terms:

x^3 - 18x^2 + 81x - 226 = 0

Now, we can solve this cubic equation by factoring, using synthetic division, or by using numerical methods such as Newton's method. However, the exact solution is quite complex and involves complex numbers.