Solving magic square results in incorrect answer

Question

I'm trying to help my daughter with her homework. I'm not looking for an answer, but the process.

She has been asked to solve this:

[ [   ?,  36,   ? ]
  [   9,   6,   4 ]
  [ -12,   ?,   ? ] ]

My approach was to substitute letters for the missing values:

[ [   A,  36,   B ]
  [   9,   6,   4 ]
  [ -12,   C,   D ] ]

Then I could solve for the unknowns:

  9 +  6 + 4 = 19
  A + 36 + B = 19
-12 +  C + D = 19
...

Solving the equations resulted in most of the rows, columns and diagonals adding up to 19 - however, not all did. I ended up with:

A = -42
B = 25
C = -24
D = 55

I'm not clear where I'm going wrong.

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My Math knowledge is very poor, simple clear answers will be preferred over complex answers.

Answer 1

As per the comments, the products, not the sums, of the rows and columns should be the same.

Apart from that, I think it's a bit cumbersome to introduce so many variables and equations. Just solve the values one at a time. For example, the second row has product $4\cdot6\cdot9$, so the missing entry in the second column must be $1$, etc.