Solve the equation x² − 5x + 6 = 0

Answer: \(x=2\) or \(x=3\).

Step-by-step:

1. Look for two numbers whose product is \(6\) and whose sum is \(-5\): \[ (-2)(-3)=6,\qquad (-2)+(-3)=-5. \]

2. Factor the quadratic: \[ x^2-5x+6=(x-2)(x-3). \]

3. Use the zero-product property: \[ (x-2)(x-3)=0 \] so either \[ x-2=0 \quad\text{or}\quad x-3=0. \]

4. Therefore: \[ x=2 \quad\text{or}\quad x=3. \]

Check:

• For \(x=2\): \(2^2-5(2)+6=4-10+6=0\).
• For \(x=3\): \(3^2-5(3)+6=9-15+6=0\).

Both values work.