How exactly is this equation for insertion sort time complexity solved so that it shows it is linear?
So you question is how to go from:

T(n)= c1(n)+c2(n−1)+c4(n−1)+c5(n−1)+c8(n−1)


to

T(n)= (c1+c2+c4+c5+c8)n−(c2+c4+c5+c8)


Step 1 (Expand the statement):

T(n)= c1(n)+c2(n)−c2+c4(n)−c4+c5(n)−c5+c8(n)−c8


Step 2 (Group similar elements):

T(n)= c1(n)+c2(n)+c4(n)+c5(n)+c8(n)−c2-c4-c5-c8


Step 3 (Find the factors):

T(n)= (c1+c2+c4+c5+c8)n−(c2+c4+c5+c8)