Solve the equation x² − 5x + 6 = 0

Answer: \(\boxed{x=2 \text{ or } x=3}\)

Key steps

Factor the quadratic:

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

This works because \(-2\cdot(-3)=6\) and \(-2+(-3)=-5\).

Now use the zero-product rule:

\[ (x-2)(x-3)=0 \]

So either

\[ x-2=0 \quad\Rightarrow\quad x=2 \]

or

\[ x-3=0 \quad\Rightarrow\quad x=3 \]

Check

\[ 2^2-5\cdot2+6=4-10+6=0 \]

\[ 3^2-5\cdot3+6=9-15+6=0 \]

Both solutions are correct.