Increasingly, real-time systems are being used in applications that contain tasks that have deadlines and require predictable performance. Many complex real-time applications require modern operating systems capable of scheduling multiple classes of tasks in an integrated way. These applications require scheduling that result in high utilization of available processing power to accommodate as many tasks as possible while satisfying the required deadlines of each task. In this paper, we propose a combined heuristic approach to schedule a set of independent soft and hard real-time tasks in multiprocessor computing systems. Each of these tasks is characterized by its arrival time, deadline and required processing power. The proposed approach distributes the total available processing power of any processor, if it is needed and possible, among more than one task, while ensuring that hard real-time tasks are given higher priority and enough processing power to meet deadlines. This strategy can be used as a tool to efficiently guide scheduling processes. In addition, it can help to optimize processor utilization and maintain higher success ratios by maximizing the schedulability of soft tasks without jeopardizing the schedulability of hard tasks.