To solve the equation \( 27 \cdot 125 \cdot 8 \cdot (49 - 6x) = 27000 \), we can start by simplifying the left side.
First, calculate the product of the constants:
\[ 27 \cdot 125 \cdot 8 \]
Calculating step-by-step:
- \( 27 \cdot 125 = 3375 \)
- Now, multiply \( 3375 \cdot 8 \): \[ 3375 \cdot 8 = 27000 \]
So, we rewrite the equation: \[ 27000 \cdot (49 - 6x) = 27000 \]
Next, we can divide both sides of the equation by 27000 (assuming \( 27000 \neq 0 \)): \[ 49 - 6x = 1 \]
Now, isolate \( x \): \[ 49 - 1 = 6x \] \[ 48 = 6x \] \[ x = \frac{48}{6} = 8 \]
Thus, the solution to the equation is: \[ \boxed{8} \]
