1. **State the problem:** Make $x$ the subject of the formula given by $$2y(6x + 1) = 5z$$. 2. **Expand the left side:** Use the distributive property to expand: $$2y \times 6x + 2y \times 1 = 5z$$ which simplifies to $$12yx + 2y = 5z$$. 3. **Isolate the term with $x$:** Subtract $2y$ from both sides: $$12yx + \cancel{2y} - \cancel{2y} = 5z - 2y$$ which simplifies to $$12yx = 5z - 2y$$. 4. **Solve for $x$:** Divide both sides by $12y$: $$\frac{12yx}{\cancel{12y}} = \frac{5z - 2y}{12y}$$ which simplifies to $$x = \frac{5z - 2y}{12y}$$. **Final answer:** $$x = \frac{5z - 2y}{12y}$$