1. **State the problem:** Factorise the expression $$x^2 - 6x + 2x^2 + 7$$. 2. **Combine like terms:** First, combine the terms with $$x^2$$. $$x^2 + 2x^2 = 3x^2$$ So the expression becomes: $$3x^2 - 6x + 7$$ 3. **Factorise the quadratic:** The expression is now $$3x^2 - 6x + 7$$. We look for factors of $$3 \times 7 = 21$$ that add up to $$-6$$. The pairs are (1, 21), (3, 7), but none add to $$-6$$. 4. **Check discriminant:** To see if it factorises over the reals, calculate the discriminant: $$\Delta = b^2 - 4ac = (-6)^2 - 4 \times 3 \times 7 = 36 - 84 = -48$$ Since $$\Delta < 0$$, the quadratic does not factorise over the real numbers. 5. **Conclusion:** The expression $$3x^2 - 6x + 7$$ cannot be factorised into real linear factors. **Final answer:** The expression is already simplified and cannot be factorised further over the real numbers.