Solve the equation x² − 5x + 6 = 0

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

How to see it:

Factor the quadratic by finding two numbers that:

• multiply to the constant term \(6\),
• add to the middle coefficient \(-5\).

Those numbers are \(-2\) and \(-3\), because

\[ (-2)(-3)=6,\qquad (-2)+(-3)=-5. \]

So

\[ x^2-5x+6=(x-2)(x-3). \]

Set each factor equal to zero:

\[ x-2=0 \quad\Rightarrow\quad x=2, \] \[ x-3=0 \quad\Rightarrow\quad x=3. \]

Check:

\[ 2^2-5(2)+6=4-10+6=0, \] \[ 3^2-5(3)+6=9-15+6=0. \]

Both work, so the solutions are \(\boxed{x=2,\;3}\).