To find the common solution set for the inequalities x2−4x≤12 and x2−2x≥15, we'll begin by rewriting them in a standard form: ‌x2−4x−12≤0 ‌x2−2x−15≥0 Next, we factor each equation: ‌(x−6)(x+2)≤0 ‌(x−5)(x+3)≥0 Now, we determine the solution sets for each inequality: For (x−6)(x+2)≤0, the interval is x∈[−2,6]. For (x−5)(x+3)≥0, the intervals are x∈(−∞,−3]∪[5,∞). To find the common solution set, we identify where these intervals overlap: The intersection of [−2,6] and (−∞,−3]∪[5,∞) is x∈[5,6]. Thus, the common solution set for the given inequalities is x∈[5,6].