Answer
$15-13t+2t^2$
Work Step by Step
Using $(a+b)(c+d)=ac+ad+bc+bd$ or the product of $2$ binomials, the given expression, $
(3-2t)(5-t)
$, is equivalent to
\begin{array}{l}\require{cancel}
3(5)+3(-t)-2t(5)-2t(-t)
\\\\=
15-3t-10t+2t^2
\\\\=
15-13t+2t^2
.\end{array}