I'm trying to solve this problem for partial fraction expansion and then apply laplace. I found A, B, and C. however, the bottom part, I'm trying to put every s=0 left side and right side; and substitute A,B,C for the found values for the right side. I'm not getting the right value for D.

TO s ( S + 2 ) ( s + 3 ) 2 S= 0 ; A=_10 - -9 A S = -2 ; (-2 ) ( - 2+ 3) (- 2 ) ( 1 ) 2 - 2 1 = 10/ - 2 = - 5 S = - 3 ( - 3 ) ( - 3 + 2 ) C = 10 1 3 ( - 3 ) ( - 1 ) (8 3 10 = A +B + C D s ( /s +2 ) ( 5 + 3 ) 2 S 5+ 2 (5+3 ) ( 5+ 3 ) 2