Factor the following equation to solve for "x"; x^{2} - 8x - 20 = 0

X² - 8x - 20 = 0

Factor the left side:

(x + 2) (x - 10) = 0

That's a true statement if (x = - 2) or if (x = 10), so those are your solutions.

x = - 2

x = 10

By the way ... you don't factor an equation. You can only factor an expression.