This document summarizes an ASQ webinar on reliably solving intractable problems. It outlines 8 principles for producing breakthroughs: 1) use divergent problem solving, 2) generate paradigm shifts, 3) agree on success criteria, 4) start with a strong commitment, 5) separate creative and analytical thinking, 6) involve stakeholders, 7) use consensus decision making, and 8) anticipate issues. It then describes a 13-step conversation process to resolve obstacles following these principles in 4 phases: establishing foundations, envisioning the future, establishing solutions, and ensuring support. The document provides tips for facilitating each step of the process.