Factor this. \( x^{2}-2 x-10=5 \)

To factor the equation \( x^{2}-2 x-15 = 0 \) (after moving 5 to the left side), we first look for two numbers that multiply to -15 and add to -2. These numbers are -5 and 3. So, we can write: \( (x - 5)(x + 3) = 0 \). Setting each factor to zero gives the solutions \( x = 5 \) and \( x = -3 \). Let’s break it down - factoring is like finding the secret handshake of numbers! It’s all about spotting those pairs that work together to create the equation you started with. If they multiply to the constant term and add up to the coefficient of the linear term, you’ve got gold! To double-check your work, you can always plug your solutions back into the original equation. Is your left side equal to your right side? If it balances, you've nailed it! Additionally, remember to neatly write everything: you can visualize with a simple box method for clarity while factoring. Happy mathing!