1. **State the problem:** Factorise the quadratic expression $10x^2 + 19x + 6$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two numbers that multiply to $a \times c$ and add to $b$. 3. **Calculate the product and sum:** Here, $a=10$, $b=19$, $c=6$. So, $a \times c = 10 \times 6 = 60$. 4. **Find two numbers that multiply to 60 and add to 19:** These numbers are 15 and 4 because $15 \times 4 = 60$ and $15 + 4 = 19$. 5. **Rewrite the middle term using these numbers:** $$10x^2 + 15x + 4x + 6$$ 6. **Group terms:** $$(10x^2 + 15x) + (4x + 6)$$ 7. **Factor each group:** $$5x(2x + 3) + 2(2x + 3)$$ 8. **Factor out the common binomial:** $$(5x + 2)(2x + 3)$$ **Final answer:** The factorised form of $10x^2 + 19x + 6$ is $$(5x + 2)(2x + 3)$$.