Solve for x over the real numbers:
x^2 - 4 x - 5 = 0
The left hand side factors into a product with two terms:
(x - 5) (x + 1) = 0
Split into two equations:
x - 5 = 0 or x + 1 = 0
Add 5 to both sides:
x = 5 or x + 1 = 0
Subtract 1 from both sides:
Answer: x = 5 or x = -1