1. **State the problem:** Solve the equation $$\frac{(5x+6)^2}{5} = 4$$ for $x$. 2. **Isolate the squared term:** Multiply both sides by 5 to eliminate the denominator. $$\cancel{5} \times \frac{(5x+6)^2}{\cancel{5}} = 4 \times 5$$ which simplifies to $$(5x+6)^2 = 20$$ 3. **Take the square root of both sides:** Remember to consider both positive and negative roots. $$5x + 6 = \pm \sqrt{20}$$ Simplify $\sqrt{20}$: $$\sqrt{20} = \sqrt{4 \times 5} = 2\sqrt{5}$$ So, $$5x + 6 = \pm 2\sqrt{5}$$ 4. **Solve for $x$:** Subtract 6 from both sides. $$5x = -6 \pm 2\sqrt{5}$$ Divide both sides by 5: $$x = \frac{-6 \pm 2\sqrt{5}}{5}$$ 5. **Final answer:** $$x = \frac{-6 + 2\sqrt{5}}{5} \quad \text{or} \quad x = \frac{-6 - 2\sqrt{5}}{5}$$ This gives the two solutions for $x$.