Let's solve the given quadratic equation step-by-step:

\[ x^2 - x - (3x - 3) = 0 \]

First, distribute the negative sign through the parentheses:

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

Combine like terms:

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

Now, we have a standard quadratic equation in the form \( ax^2 + bx + c = 0 \). To solve this, we can either factor the quadratic equation, complete the square, or use the quadratic formula. In this case, let's try factoring.

We need to find two numbers that multiply to \( 3 \) (the constant term) and add up to \( -4 \) (the coefficient of the linear term). These numbers are \( -1 \) and \( -3 \).

So, we can factor the quadratic equation as follows:

\[ (x - 1)(x - 3) = 0 \]

To find the solutions, set each factor equal to zero:

\[ x - 1 = 0 \quad \text{or} \quad x - 3 = 0 \]

Solve for \( x \):

\[ x = 1 \quad \text{or} \quad x = 3 \]

Therefore, the solutions to the equation \( x^2 - x - (3x - 3) = 0 \) are:

\[ x = 1 \quad \text{and} \quad x = 3 \]