Prove using mathematical induction: 5²ⁿ⁺¹*2ⁿ⁺² + 3ⁿ⁺²*2²ⁿ⁺¹ is divisible by 19

Dear student 

Dear student
5^(2n+1)*2^(n+2) + 3^(n+2)*2^(2n+1) is divisible by 19
Put n =1 and check  
Yes it is divisible by 19 
Put n = k 
5^(2k+1)*2^(k+2) + 3^(k+2)*2^(2k+1) = 19J 
Put n = k+1 
5^(2k+3)*2^(k+3) + 3^(k+3)*2^(2k+3) 
=> 25*4*5^(2k+1)*2^(k+2) + 3*4* 3^(k+2)*2^(2k+1) 
100*5^(2k+1)*2^(k+2) + 12*3^(k+2)*2^(2k+1) 
which is divisible by 19 
Hence prooved