still confused on 'Differentiate (3x2 + 2)^4(4 - 5x)^5...'

[yanarains]

Differentiate the given function and simplify your answer

(3x2 + 2)^4(4 - 5x)^5 .

The answer is in the form of

(3x2 + 2)^3(4 - 5x)^4(Ax^2 + 96x - 50) .

Find the value of A.

[4(3x^2+2)^3(6x)](4-5x)^5+(3x^2+2)^4 [5(4-5x)^4(-5)].......fix this line

24x(3x^2+2)^3(4-5x)^5-25(3x^2+2)^4(4-5x)]

this can be shown as
24A^3B^5 - 25A^4B^4 : then i simplify the answer

A^3B^4 (24B-25A)
=(3x^2+2)^3 (4-5x)^4 [24(4-5x)-25(3x^2+2)]
=(3x^2+2)^3(4-5x)^4[-75x^2-120x+46]

the answer should look like this (3x2 + 2)^3(4 - 5x)^4(Ax^2 + 96x - 50)
I am looking for A: My last two numbers don't match the rest of the answer so A doesn't not =75x^2
what is the next step of this problem in order to make my answer match the answer given?
Hope that makes sense.
Thanks:0

 

[pka]

\(\displaystyle \L \begin{array}{rcl}
D_x \left[ {\left( {3x^2 + 2} \right)^4 \left( {4 - 5x} \right)^5 } \right] & = & (4)(6x)\left( {3x^2 + 2} \right)^3 \left( {4 - 5x} \right)^5 + \left( {3x^2 + 2} \right)^4 \left[ {(5)( - 5)\left( {4 - 5x} \right)^4 } \right] \\
& = & \left( {3x + 2} \right)^3 \left( {4 - 5x} \right)^4 \left[ {(4)(6x)\left( {4 - 5x} \right) + \left( {3x^2 + 2} \right)\left[ {(5)( - 5)} \right]} \right] \\
& = & \left( {3x^2 + 2} \right)^3 \left( {4 - 5x} \right)^4 \left[ {\left( {24x} \right)\left( {4 - 5x} \right) - 25\left( {3x^2 + 2} \right)} \right] \\
\end{array}\)

Now you finish.