Video narration
You know x, but turning a quadratic into factors can feel like a guessing game. Find a number pair with product six and sum negative five. Here: x squared minus five x plus six equals zero. The pair is negative two and negative three: their product is six, their sum negative five. Split the middle term: x squared minus two x minus three x plus six. Group: x times the quantity x minus two, minus three times the quantity x minus two. That factorises the quadratic-rewrites it as the quantity x minus two times the quantity x minus three, equal to zero. The zero-product rule means if the product is zero, one factor must be zero. So x minus two equals zero, or x minus three equals zero. The matching pair is negative two and negative three; the solutions are x equals two or x equals three.