Solve the equation x² − 5x + 6 = 0

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

Key steps:
Factor the quadratic by finding two numbers that multiply to \(6\) and add to \(-5\): these are \(-2\) and \(-3\).

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

So:

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

A product is zero only if at least one factor is zero:

\[ x-2=0 \quad\text{or}\quad x-3=0 \]

\[ x=2 \quad\text{or}\quad x=3 \]

Check:
For \(x=2\): \(4-10+6=0\).
For \(x=3\): \(9-15+6=0\). Both work.

Principle: For \(x^2+bx+c=0\), look for two numbers whose product is \(c\) and whose sum is \(b\). Then write the equation as a product and set each factor equal to zero.