1. **State the problem:** Solve the equation $$(x-1)(x+1) = 4x - 5$$ for $x$. 2. **Use the distributive property (FOIL) on the left side:** $$ (x-1)(x+1) = x^2 + x - x - 1 = x^2 - 1 $$ 3. **Rewrite the equation:** $$ x^2 - 1 = 4x - 5 $$ 4. **Bring all terms to one side to set the equation to zero:** $$ x^2 - 1 - 4x + 5 = 0 $$ 5. **Simplify:** $$ x^2 - 4x + 4 = 0 $$ 6. **Recognize this as a perfect square trinomial:** $$ (x - 2)^2 = 0 $$ 7. **Solve for $x$ by taking the square root of both sides:** $$ \sqrt{(x - 2)^2} = \sqrt{0} $$ $$ |x - 2| = 0 $$ 8. **Therefore:** $$ x - 2 = 0 $$ $$ x = 2 $$ **Final answer:** $$ x = 2 $$