Alternatively, working with each of the powers of x from $x}^{3$ down to $x}^{0$ (i.e. the constant term), match the terms in the first and second bracketed expressions which will multiply to give that power of x and add them together, thus:
Given: $(2x-3)({x}^{2}+5x-3)$ $x}^{3}:2x\times {x}^{2}=2{x}^{3$ $x}^{2}:(2x\times 5x)+(-3\times {x}^{2})=10{x}^{2}-3{x}^{2}=7{x}^{2$ ${x}^{1}:(2x\times -3)+(-3\times 5x)=-6x-15x=-21x$ ${x}^{0}:-3\times -3=9$
Added, give $2{x}^{3}+7{x}^{2}-21x+9$