Step 1: First we have to write polynomials in descending order.

$$ \begin{aligned} P(x) &= -2x+3 \\ Q(x) &= x+3 \\ \end{aligned} $$

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

$$ \begin{aligned} \left( \color{blue}{ -2x+3}\right) \cdot \left( \color{orangered}{ x+3}\right) &= \underbrace{ \left( \color{blue}{-2x} \right) \cdot \color{orangered}{x} }_{\text{FIRST}} + \underbrace{ \left( \color{blue}{-2x} \right) \cdot \color{orangered}{3} }_{\text{OUTER}} + \underbrace{ \color{blue}{3} \cdot \color{orangered}{x} }_{\text{INNER}} + \underbrace{ \color{blue}{3} \cdot \color{orangered}{3} }_{\text{LAST}} = \\ &= -2x^2 + \left( -6x\right) + 3x + 9 = \\ &= -2x^2 + \left( -6x\right) + 3x + 9 = \\ &= -2x^2-3x+9; \end{aligned} $$

Polynomial Operations Calculator