1. **State the problem:** Factorise the quadratic expression $$12k^2 - 17k - 7$$. 2. **Identify coefficients:** Here, $$a = 12$$, $$b = -17$$, and $$c = -7$$. 3. **Calculate the product of $$a$$ and $$c$$:** $$12 \times (-7) = -84$$. 4. **Find two numbers that multiply to $$-84$$ and add to $$-17$$:** These numbers are $$-21$$ and $$4$$ because $$-21 \times 4 = -84$$ and $$-21 + 4 = -17$$. 5. **Rewrite the middle term using these numbers:** $$12k^2 - 21k + 4k - 7$$. 6. **Group terms:** $$(12k^2 - 21k) + (4k - 7)$$. 7. **Factor each group:** $$3k(4k - 7) + 1(4k - 7)$$. 8. **Factor out the common binomial:** $$(3k + 1)(4k - 7)$$. 9. **Final factorised form:** $$12k^2 - 17k - 7 = (3k + 1)(4k - 7)$$.