Choice A is the correct answer.

1. Equation: $x + x^2 = 42$.
2. Standard Form: $x^2 + x - 42 = 0$.
3. Factor: $(x + 7)(x - 6) = 0$.
4. Solutions: $x = -7$ or $x = 6$.

Choice B is incorrect because signs are swapped. Choice C is incorrect because it misses the negative solution. Choice D is incorrect.