Solve $x^2-5x+6=0$

Step-by-step solution

1. Step 1 · Standard form
   $$x^2-5x+6=0$$

   The quadratic is already written as ax² + bx + c = 0 with a = 1.

2. Step 2 · Factoring a monic trinomial
   $$(x-2)(x-3)=0$$

   Two numbers multiplying to 6 and adding to −5 are −2 and −3.

3. Step 3 · Zero product property
   $$x-2=0\text{or}x-3=0$$

   A product is zero only when one of its factors is zero.

4. Step 4 · Solve each factor
   $$x=2,x=3$$

   Both roots check in the original equation.