Does anyone feel like finding a partial fraction decomposition?!

(3x^2 + 49)/ x(x+7)^2

Been working at this for hours... Help! My assignment says to write the partial fraction decomposition. Any of you Algebra whizzes want to help a poor kid in need?!

A / x + B / (x + 7) + C / (x + 7)^2 = (3x^2 + 49) / (x * (x + 7)^2)

A * (x + 7)^2 + B * x * (x + 7) + C * x = 3x^2 + 0x + 49
A * (x^2 + 14x + 49) + B * (x^2 + 7x) + Cx = 3x^2 + 0x + 49
Ax^2 + Bx^2 + 14Ax + 7Bx + Cx + 49A = 3x^2 + 0x + 49

Ax^2 + Bx^2 = 3x^2
14Ax + 7Bx + Cx = 0x
49A = 49

A = 49/49 = 1

A + B = 3
1 + B = 3
B = 2

14A + 7B + C = 0
14 * 1 + 7 * 2 + C = 0
14 + 14 + C = 0
28 + C = 0
C = -28

1 / x + 2 / (x + 7) - 28 / (x + 7)^2

A / x + B / ( x + 7 ) + C / ( x + 7 )^2 = (3x^2 + 49 ) / [ x ( x + 7 )^2 ]

find A, B and C

A / x + ( Bx + C ) / ( x + 7 )^2
= [A(x + 7 )^2 + (Bx^2 + Cx ) ] / [ x(x + 7 )^2 ]

A + B = 3
14 + 7B + C = 0
49A = 49
A = 1, B = 2, C = - 28