Solve the equation x² − 5x + 6 = 0

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

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

Now use the zero-product rule: if \[ (x-2)(x-3)=0, \] then one of the factors must equal zero:

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

Check:

• \(2^2-5\cdot2+6=4-10+6=0\)
• \(3^2-5\cdot3+6=9-15+6=0\)

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