sum of multiple of two binomial cofficinet

I’m trying to show this equality. I try to expand it but I have no idea to go on.Thanks in advance for your help.
The equality is
$sum_{i=0}^{n-1}(2i+1){n-2choose n-1-i}{nchoose i+1}=2(n-1){2n-3choose n}+{2(n-1)choose n}+2{2n-3choose n-1}$
I write the left side of equality as bellow
$sum_{i=0}^{n-1}(2i+1){n-2choose n-1-i}{nchoose i+1}=2$sum_{i=0}^{n-1}i{n-2choose n-1-i}{nchoose i+1}+$sum_{i=0}^{n-1}(2i+1){n-2choose n-1-i}{nchoose i+1}=2({n-2choose n-2}{nchoose 2}+2{n-2choose n-3}{nchoose 3}+3{n-2choose n-4}{nchoose 4}+…+(n-1){n-2choose 0}{nchoose n})+{2(n-1)choose n}$
I appreciate help me to continue.