x² + 7x + 12 = 0
To factor we need two numbers which add to 7 and multiply to 12. In other words, guess the answer. Here it's easy, 3 and 4.
(x + 3)(x + 4) = 0
When a product is zero, one of the factors must be zero.
x + 3 = 0 or x + 4 = 0
x = -3 or x = -4
Answer: x = -3 or x = -4
