Solving by factoring

#factoring#roots#quadratic

Statement

Solve in $\mathbb{R}$ the equation
$x^2-5x+6=0.$

Hint

Find two numbers whose sum is $5$ and product is $6$ .

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Factoring. $x^2-5x+6=(x-2)(x-3)$ .

Roots. $(x-2)(x-3)=0\iff x=2$ or $x=3$ .

Conclusion. $x\in\{2,3\}$ .

Remark. This is the fastest method when the roots are integers (Vieta's formulas in reverse).