1. **State the problem:** Factor and solve for the x-intercepts of the quadratic function $$y=3x^2 - 36x + 60$$. 2. **Formula and rules:** To find x-intercepts, set $$y=0$$ and solve for $$x$$. 3. **Set the equation to zero:** $$3x^2 - 36x + 60 = 0$$ 4. **Factor out the greatest common factor (GCF):** $$3(x^2 - 12x + 20) = 0$$ 5. **Divide both sides by 3:** $$\cancel{3}(x^2 - 12x + 20) = \cancel{3} \times 0$$ $$x^2 - 12x + 20 = 0$$ 6. **Factor the quadratic:** Find two numbers that multiply to 20 and add to -12: -10 and -2. $$x^2 - 12x + 20 = (x - 10)(x - 2)$$ 7. **Set each factor equal to zero:** $$x - 10 = 0 \Rightarrow x = 10$$ $$x - 2 = 0 \Rightarrow x = 2$$ 8. **Final answer:** The x-intercepts are $$x=10$$ and $$x=2$$.