To solve the equation \( x^2 - 4x + 4 = 3(x-2) \), we first simplify both sides.

Start by rewriting the equation:

\[
x^2 - 4x + 4 = 3(x - 2)
\]

Next, simplify the right side:

\[
3(x - 2) = 3x - 6
\]

Now we have:

\[
x^2 - 4x + 4 = 3x - 6
\]

Next, we move all terms to one side of the equation:

\[
x^2 - 4x + 4 - 3x + 6 = 0
\]

Combine like terms:

\[
x^2 - 7x + 10 = 0
\]

Now, we need to factor the quadratic. We can look for two numbers that multiply to \(10\) (the constant term) and add up to \(-7\) (the coefficient of \(x\)). These numbers are \(-5\) and \(-2\). Thus, we can factor the equation as:

\[
(x - 5)(x - 2) = 0
\]

Setting each factor to zero gives us the potential solutions:

\[
x - 5 = 0 \quad \Rightarrow \quad x = 5
\]
\[
x - 2 = 0 \quad \Rightarrow \quad x = 2
\]

So the solutions to the equation \( x^2 - 4x + 4 = 3(x - 2) \) are:

\[
x = 5 \quad \text{and} \quad x = 2
\]