To find the values of A, B, and C, we should start by getting the left side of the equation to look like the formatting on the right side of the equation.
First, use the distributive property for each set of parentheses. The equation shown should appear as:
[tex]\frac{72z-36x-6x-54z-3x-18y}{3}=A(5x+By+Cz)[/tex]
Next, combine like-terms and rearrange each term by alphabetical order to match the formatting of A(5x+By+Cz):
[tex]\frac{-45x-18y+18z}{3}=A(5x+By+Cz)[/tex]
Now, find the greatest common factor from all terms:
[tex]\frac{-9(5x+2y-2z)}{3} =A(5x+By+Cz)[/tex]
Divide -9 by three, to get the final equation:
[tex]-3(5x+2y-2z) =A(5x+By+Cz)[/tex]
All that is left to do is to find the presented values for A, B, and C.
C = -3, B = 2, and C = -2