To solve this equation, we can start by simplifying both sides of the equation.

On the left side, we have (x - 1)^3. This can be expanded using the binomial theorem:

(x - 1)^3 = x^3 - 3x^2 + 3x - 1

On the right side, we have (x - 1)^8. This can also be expanded using the binomial theorem:

(x - 1)^8 = x^8 - 8x^7 + 28x^6 - 56x^5 + 70x^4 - 56x^3 + 28x^2 - 8x + 1

Now we have the equation:

x^3 - 3x^2 + 3x - 1 = x^8 - 8x^7 + 28x^6 - 56x^5 + 70x^4 - 56x^3 + 28x^2 - 8x + 1

Next, we can combine like terms and simplify the equation:

x^8 - 8x^7 + 28x^6 - 56x^5 + 70x^4 - 56x^3 + 28x^2 - 8x + 1 - x^3 + 3x^2 - 3x + 1 = 0

x^8 - 8x^7 + 28x^6 - 56x^5 + 70x^4 - 57x^3 + 31x^2 - 11x + 2 = 0

At this point, it is difficult to find the exact solutions to this equation. However, we can use numerical methods or graphing to approximate the solutions.