1. **State the problem:** Solve the equation $$0 = (3x - 4)^2 - 7(3x - 4) + 10$$ for $x$. 2. **Use substitution:** Let $$y = 3x - 4$$ to simplify the equation to $$0 = y^2 - 7y + 10$$. 3. **Factor the quadratic:** Find factors of 10 that add up to -7. These are -5 and -2, so: $$y^2 - 7y + 10 = (y - 5)(y - 2)$$. 4. **Set each factor to zero:** $$y - 5 = 0 \implies y = 5$$ $$y - 2 = 0 \implies y = 2$$ 5. **Back-substitute for $x$:** Recall $y = 3x - 4$, so: - For $y = 5$: $$3x - 4 = 5 \implies 3x = 9 \implies x = 3$$ - For $y = 2$: $$3x - 4 = 2 \implies 3x = 6 \implies x = 2$$ 6. **Final answer:** The solutions are $$x = 3$$ and $$x = 2$$.