The distributive property for multiplication is given by,
[tex]a(b+c+d)=ab+ac+ad[/tex]Using the above property, the given polynomial can be simplified as,
[tex]\begin{gathered} (3x+2)(-3x^2-7x+3) \\ =3x(-3x^2-7x+3)+2(-3x^2-7x+3) \\ =3x\times(-3x^2)+3x\times(-7x)+3x\times3+2\times(-3x^2)+2\times(-7x)+2\times3 \\ =-9x^2-21x+9x-6x^2-14x+6 \end{gathered}[/tex]Now, comine the like terms and arrange the terms in the desceding order in which the exponents of variables comes.
[tex]\begin{gathered} (-9x^2-6x^2)-21x-14x+6 \\ =-15x^2-35x+6 \\ \text{Therefore, the standard simplified form of the polynomial is} \\ -15x^2-35x+6 \end{gathered}[/tex]