1. The problem is to verify if the equation $$(7x+3)^2 = (7x+4)(7x-4)$$ is correct and solve for $x$ if it is. 2. First, expand both sides: Left side: $$(7x+3)^2 = (7x)^2 + 2 \cdot 7x \cdot 3 + 3^2 = 49x^2 + 42x + 9$$ Right side: $$(7x+4)(7x-4) = (7x)^2 - 4^2 = 49x^2 - 16$$ 3. Set the expanded forms equal: $$49x^2 + 42x + 9 = 49x^2 - 16$$ 4. Subtract $49x^2$ from both sides: $$42x + 9 = -16$$ 5. Subtract 9 from both sides: $$42x = -25$$ 6. Divide both sides by 42: $$x = \frac{-25}{42}$$ 7. The solution $x = -\frac{25}{42}$ is correct and satisfies the original equation.