1. **State the problem:** Factor the expression $$5a^2 + 10ab - 3a - 6b$$. 2. **Identify the method:** We will use factoring by grouping, which involves grouping terms to find common factors. 3. **Group terms:** Group the first two and last two terms: $$ (5a^2 + 10ab) + (-3a - 6b) $$ 4. **Factor out common factors in each group:** $$ 5a(a + 2b) - 3(a + 2b) $$ 5. **Factor out the common binomial factor:** $$ \cancel{(a + 2b)}(5a - 3) \cancel{(a + 2b)} $$ 6. **Write the final factored form:** $$ (a + 2b)(5a - 3) $$ **Answer:** The factored form of $$5a^2 + 10ab - 3a - 6b$$ is $$ (a + 2b)(5a - 3) $$.