To solve the quadratic equation \( x^2 - x = 6 \) by factoring, we first rearrange the equation to set it to zero:
\[ x^2 - x - 6 = 0 \]
Next, we need to factor the quadratic expression \( x^2 - x - 6 \). We look for two numbers that multiply to \(-6\) (the constant term) and add to \(-1\) (the coefficient of \(x\)).
The numbers that satisfy these conditions are \(-3\) and \(2\) because:
\[ -3 \cdot 2 = -6 \quad \text{and} \quad -3 + 2 = -1 \]
Now we can write the factored form of the equation:
\[ (x - 3)(x + 2) = 0 \]
Setting each factor to zero gives us the possible solutions:
- \( x - 3 = 0 \) which implies \( x = 3 \)
- \( x + 2 = 0 \) which implies \( x = -2 \)
Thus, the solution set is:
\[ { 3, -2 } \]
So, the final answer is:
\({ 3, -2 }\)