Algebra II: multi-variable equation help?!

Find the values of a, b, and c that satisfy the equation; 3ax^2 + bx + 5x + c - 7 = 12x^2 - 6x - 9

I need a mathematical and/or literal explanation for proof of the correct answers. Note that there are 3: a=__, b=__, and c=__.

equating coefficients of x^2, we get 3a =12
a =4

equating coefficients of x, we get b+5 = -6
b = -11

equating constants , c-7 = -9
c= -2

a = 4
b = -11
c = -2

3(4)x^2 + (-11)x + 5x + (-2) - 7 = 12x^2 - 6x - 9
12x^2 - 6x -9 = 12x^2 - 6x - 9