Solve for all values of x by factoring. x, squared, minus, 8, x, plus, 15, equals, 0 x 2 −8x+15= 0

Problem: Solve for $x$ in the equation $x^2 - 8x + 15 = 0$ by factoring.

Steps

1. Factor the quadratic expression (find two numbers that multiply to $15$ and add to $-8$)
   $$(x - 3)(x - 5) = 0$$
2. Apply the Zero Product Property (set each factor equal to zero)
   $$x - 3 = 0 \quad \text{or} \quad x - 5 = 0$$
3. Solve for $x$ (add the constants to both sides)
   $$x = 3 \quad \text{or} \quad x = 5$$