1. The problem is to simplify and solve the equation: $$16x^2 - (4x - 1)(4x + 1) + 2x = 7$$ 2. Recall the formula for the difference of squares: $$(a - b)(a + b) = a^2 - b^2$$ 3. Apply this to the term $(4x - 1)(4x + 1)$: $$(4x)^2 - 1^2 = 16x^2 - 1$$ 4. Substitute back into the equation: $$16x^2 - (16x^2 - 1) + 2x = 7$$ 5. Simplify inside the parentheses: $$16x^2 - 16x^2 + 1 + 2x = 7$$ 6. Combine like terms: $$1 + 2x = 7$$ 7. Subtract 1 from both sides: $$2x = 6$$ 8. Divide both sides by 2: $$x = 3$$ Final answer: $x = 3$