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In this paper, we present efficient solutions for planning motions of dual-arm manipulation and re-grasping tasks. Motion planning for such tasks on humanoid robots with a high number of degrees of freedom (DoF) requires computationally efficient approaches to determine the robot's full joint configuration at a given grasping position, i.e. solving the Inverse Kinematics (IK) problem for one or both hands of the robot. In this context, we investigate solving the inverse kinematics problem and motion planning for dual-arm manipulation and re-grasping tasks by combining a gradient-descent approach in the robot's pre-computed reachability space with random sampling of free parameters. This strategy provides feasible IK solutions at a low computation cost without resorting to iterative methods which could be trapped by joint-limits. We apply this strategy to dual-arm motion planning tasks in which the robot is holding an object with one hand in order to generate whole-body robot configurations suitable for grasping the object with both hands. In addition, we present two probabilistically complete RRT-based motion planning algorithms (J+-RRT and IK-RRT) that interleave the search for an IK solution with the search for a collision-free trajectory and the extension of these planners to solving re-grasping problems. The capabilities of combining IK methods and planners are shown both in simulation and on the humanoid robot ARMAR-III performing dual-arm tasks in a kitchen environment.