Generate 30 college-level math problems that are tailored to the subject of [quadratic factoring ]. Each problem should be formatted with small equation numbers, such as (1), (2), etc., as if they are part of a formal test or assignment prepared by a professor. The problems should be a mix of different difficulty levels, ranging from basic to more advanced concepts, ensuring a well-rounded assessment of the subject matter. It is essential that the problems are concise, clearly stated, and written in standard mathematical notation, with a strong emphasis on applying key mathematical concepts and formulas relevant to [quadractic factoring ]. Additionally, provide the complete solution set for each problem, showcasing step-by-step methods where necessary to ensure clarity and ease of understanding. The overall presentation should be neat and professional, making the problems easy to read and comprehend.