Solve x^2 - 8x + 15 = 0.

Factor the quadratic by finding two numbers whose product is 15 and whose sum is -8.

Those numbers are -3 and -5:
x^2 - 8x + 15 = (x - 3)(x - 5)

Set each factor equal to zero:
x - 3 = 0
x - 5 = 0

Solve each equation:
x = 3
x = 5

Therefore, the quadratic has two solutions.