Step 1: d2⋅vs⋅cos45∘=d1⋅(vr−vssin45∘)
They multiplied out the bracket on the right hand side:
d2⋅vs⋅cos45∘=d1⋅vr−d1⋅vssin45∘
and then they add d1 . vs sin45 each side:
d2⋅vs⋅cos45∘+d1⋅vssin45∘=d1⋅vr
Factor out the common factor(vs):
vs⋅(d2⋅cos45∘+d1sin45∘)=d1⋅vr <-- Step 2!!