In this example we are multiplying two binomials so FOIL method can be used.

$$ \begin{aligned} \left( \color{blue}{ 2n+3}\right) \cdot \left( \color{orangered}{ n-2}\right) &= \underbrace{ \color{blue}{2n} \cdot \color{orangered}{n} }_{\text{FIRST}} + \underbrace{ \color{blue}{2n} \cdot \left( \color{orangered}{-2} \right) }_{\text{OUTER}} + \underbrace{ \color{blue}{3} \cdot \color{orangered}{n} }_{\text{INNER}} + \underbrace{ \color{blue}{3} \cdot \left( \color{orangered}{-2} \right) }_{\text{LAST}} = \\ &= 2n^2 + \left( -4n\right) + 3n + \left( -6\right) = \\ &= 2n^2 + \left( -4n\right) + 3n + \left( -6\right) = \\ &= 2n^2-n-6; \end{aligned} $$

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