Complete the simplification below by finding the values of the capitalised pronumerals. $X$ is a negative number.
\[
\begin{array}{l}
\frac{6(2 a-4 c)-6(6 a-4 b)+3(4 b-8 c)}{4}=X(2 a+Y b+Z c) \\
X=\square \\
Y=\square \\
Z=\square
\end{array}
\]

Answer

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Answer

Find the values of X, Y, and Z: $\boxed{X = -3, Y = -3, Z = 4}$

Steps

Step 1 ：First, simplify the numerator of the fraction: $6(2a-4c)-6(6a-4b)+3(4b-8c) = -24a + 36b - 48c$

Step 2 ：Factor out any common factors in the simplified numerator: $-24a + 36b - 48c = -12(2a - 3b + 4c)$

Step 3 ：Divide the factored numerator by the denominator: $\frac{-12(2a - 3b + 4c)}{4} = -3(2a - 3b + 4c)$

Step 4 ：Compare the simplified expression with the right side of the equation: $-3(2a - 3b + 4c) = X(2a + Yb + Zc)$

Step 5 ：Find the values of X, Y, and Z: $\boxed{X = -3, Y = -3, Z = 4}$