1. **State the problem:** Expand the expression $$(5+6x)(3+5x)$$. 2. **Formula used:** Use the distributive property (FOIL method) for binomials: $$(a+b)(c+d) = ac + ad + bc + bd$$. 3. **Apply the formula:** $$5 \times 3 + 5 \times 5x + 6x \times 3 + 6x \times 5x$$ 4. **Calculate each term:** $$15 + 25x + 18x + 30x^2$$ 5. **Combine like terms:** $$15 + (25x + 18x) + 30x^2 = 15 + 43x + 30x^2$$ 6. **Final answer:** $$30x^2 + 43x + 15$$