1. **Problem:** Solve for $x$ and find the restricted values in the equation $$52x - 16(x-1) = 45(3x-2).$$ 2. **Formula and rules:** Use distributive property and combine like terms to simplify both sides. 3. **Step-by-step solution:** 1. Expand both sides: $$52x - 16x + 16 = 135x - 90$$ 2. Combine like terms on the left: $$36x + 16 = 135x - 90$$ 3. Move all $x$ terms to one side and constants to the other: $$36x - 135x = -90 - 16$$ 4. Simplify: $$-99x = -106$$ 5. Solve for $x$: $$x = \frac{-106}{-99} = \frac{106}{99}$$ 4. **Restricted values:** Since the equation is linear and no denominators or square roots are involved, there are no restricted values. 5. **Final answer:** $$x = \frac{106}{99}$$