1. **Problem a:** Solve the equation $x(x - 5) = 6$. 2. **Formula and rules:** Expand the left side and bring all terms to one side to form a quadratic equation: $$x^2 - 5x = 6 \implies x^2 - 5x - 6 = 0$$ 3. **Intermediate work:** Factor the quadratic: $$x^2 - 5x - 6 = (x - 6)(x + 1) = 0$$ 4. **Solutions:** Set each factor equal to zero: $$x - 6 = 0 \implies x = 6$$ $$x + 1 = 0 \implies x = -1$$ 5. **Answer:** The solutions are $x = 6$ and $x = -1$. Note: Although multiple problems were given, only the first problem is solved as per instructions.