Final answer:
The quadratic equation n² + 7n + 12 = 0 can be factored into (n + 3)(n + 4) = 0, yielding solutions n = -3 and n = -4.
Step-by-step explanation:
To solve the quadratic equation n² + 7n + 12 = 0 by factoring, we look for two numbers that multiply to give +12 (the constant term) and add up to +7 (the coefficient of the linear term). The numbers that satisfy these conditions are +3 and +4. Therefore, we can factor the quadratic as follows:
(n + 3)(n + 4) = 0
Setting each factor equal to zero gives us the solutions:
n + 3 = 0 → n = -3
n + 4 = 0 → n = -4
Thus, the solutions to the equation are n = -3 and n = -4.