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

$$ \begin{aligned} \left( \color{blue}{ 3c-5}\right) \cdot \left( \color{orangered}{ c+3}\right) &= \underbrace{ \color{blue}{3c} \cdot \color{orangered}{c} }_{\text{FIRST}} + \underbrace{ \color{blue}{3c} \cdot \color{orangered}{3} }_{\text{OUTER}} + \underbrace{ \left( \color{blue}{-5} \right) \cdot \color{orangered}{c} }_{\text{INNER}} + \underbrace{ \left( \color{blue}{-5} \right) \cdot \color{orangered}{3} }_{\text{LAST}} = \\ &= 3c^2 + 9c + \left( -5c\right) + \left( -15\right) = \\ &= 3c^2 + 9c + \left( -5c\right) + \left( -15\right) = \\ &= 3c^2+4c-15; \end{aligned} $$

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