1. **State the problem:** Expand and fully simplify the expression $$(2x - 1)(x - 5)(x + 6)$$. 2. **Formula and rules:** To expand the product of multiple binomials, first multiply two binomials using the distributive property (FOIL method), then multiply the result by the remaining binomial. 3. **Step 1: Multiply the first two binomials:** $$(2x - 1)(x - 5) = 2x \cdot x + 2x \cdot (-5) - 1 \cdot x - 1 \cdot (-5)$$ $$= 2x^2 - 10x - x + 5 = 2x^2 - 11x + 5$$ 4. **Step 2: Multiply the result by the third binomial:** $$(2x^2 - 11x + 5)(x + 6) = 2x^2 \cdot x + 2x^2 \cdot 6 - 11x \cdot x - 11x \cdot 6 + 5 \cdot x + 5 \cdot 6$$ $$= 2x^3 + 12x^2 - 11x^2 - 66x + 5x + 30$$ 5. **Step 3: Combine like terms:** $$2x^3 + (12x^2 - 11x^2) + (-66x + 5x) + 30 = 2x^3 + x^2 - 61x + 30$$ **Final answer:** $$\boxed{2x^3 + x^2 - 61x + 30}$$