To solve the equation

\[
(x-2)^{2} - (x+2)(x^{2}-2x+4) + (2x-5)(3x-3) = 0,
\]

we'll simplify each term step by step.

1. **Expand \((x-2)^{2}\):**
\[
(x-2)^{2} = x^{2} - 4x + 4.
\]

2. **Expand \((x+2)(x^{2}-2x+4)\):**
\[
(x+2)(x^{2}-2x+4) = x \cdot (x^{2}-2x+4) + 2 \cdot (x^{2}-2x+4) = x^{3} - 2x^{2} + 4x + 2x^{2} - 4x + 8 = x^{3} + 8.
\]

3. **Expand \((2x-5)(3x-3)\):**
\[
(2x-5)(3x-3) = 2x \cdot 3x - 2x \cdot 3 - 5 \cdot 3x + 5 \cdot 3 = 6x^{2} - 6x - 15x + 15 = 6x^{2} - 21x + 15.
\]

4. **Combine all the expansions:**
Substitute the expanded forms back into the equation:
\[
(x^{2} - 4x + 4) - (x^{3} + 8) + (6x^{2} - 21x + 15) = 0.
\]

5. **Combine like terms:**
\[
-x^{3} + (1 + 6)x^{2} + (-4 - 21)x + (4 - 8 + 15) = 0,
\]
simplify to:
\[
-x^{3} + 7x^{2} - 25x + 11 = 0.
\]

6. **Multiply by -1 to make the leading coefficient positive:**
\[
x^{3} - 7x^{2} + 25x - 11 = 0.
\]

Now, we can solve the polynomial equation \(x^{3} - 7x^{2} + 25x - 11 = 0\) using numerical methods or synthetic division to find its roots.

You can use software or further factorization to find the specific roots of this cubic equation.