1. **State the problem:** Factorise the quadratic expression $6x^2 + 7x - 20$. 2. **Recall the formula and method:** To factorise 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:** Here, $a = 6$, $b = 7$, and $c = -20$. So, $a \times c = 6 \times (-20) = -120$. 4. **Find two numbers:** We need two numbers that multiply to $-120$ and add to $7$. These numbers are $15$ and $-8$ because $15 \times (-8) = -120$ and $15 + (-8) = 7$. 5. **Rewrite the middle term:** Rewrite $7x$ as $15x - 8x$: $$6x^2 + 15x - 8x - 20$$ 6. **Group terms:** Group the terms in pairs: $$(6x^2 + 15x) + (-8x - 20)$$ 7. **Factor each group:** $$3x(2x + 5) - 4(2x + 5)$$ 8. **Factor out the common binomial:** $$(3x - 4)(2x + 5)$$ **Final answer:** The factorised form of $6x^2 + 7x - 20$ is $$ (3x - 4)(2x + 5) $$.