Multiply polynomial $ \, \color{blue}{ -5x+3 } \, $ by $ \, \color{orangered}{ 3x+4 }$.

$$ \left( \color{blue}{-5x+3} \right) \cdot \left( \color{orangered}{3x+4} \right) = -15x^2-11x+12 $$

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

$$ \begin{aligned} \left( \color{blue}{ -5x+3}\right) \cdot \left( \color{orangered}{ 3x+4}\right) &= \underbrace{ \left( \color{blue}{-5x} \right) \cdot \color{orangered}{3x} }_{\text{FIRST}} + \underbrace{ \left( \color{blue}{-5x} \right) \cdot \color{orangered}{4} }_{\text{OUTER}} + \underbrace{ \color{blue}{3} \cdot \color{orangered}{3x} }_{\text{INNER}} + \underbrace{ \color{blue}{3} \cdot \color{orangered}{4} }_{\text{LAST}} = \\ &= -15x^2 + \left( -20x\right) + 9x + 12 = \\ &= -15x^2 + \left( -20x\right) + 9x + 12 = \\ &= -15x^2-11x+12; \end{aligned} $$

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