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

$$ \begin{aligned} \left( \color{blue}{ -3x+4}\right) \cdot \left( \color{orangered}{ 3x-5}\right) &= \underbrace{ \left( \color{blue}{-3x} \right) \cdot \color{orangered}{3x} }_{\text{FIRST}} + \underbrace{ \left( \color{blue}{-3x} \right) \cdot \left( \color{orangered}{-5} \right) }_{\text{OUTER}} + \underbrace{ \color{blue}{4} \cdot \color{orangered}{3x} }_{\text{INNER}} + \underbrace{ \color{blue}{4} \cdot \left( \color{orangered}{-5} \right) }_{\text{LAST}} = \\ &= -9x^2 + 15x + 12x + \left( -20\right) = \\ &= -9x^2 + 15x + 12x + \left( -20\right) = \\ &= -9x^2+27x-20; \end{aligned} $$

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