7(8z-10)-25(4z+3)=3(5z-6)+z-7 z=

Let's solve the equation step by step. The equation is: \[ 7(8z - 10) - 25(4z + 3) = 3(5z - 6) + z - 7 \] 1. Distribute on both sides: Left side: \[ 7(8z) - 7(10) - 25(4z) - 25(3) = 56z - 70 - 100z - 75 \] Combine like terms: \[ 56z - 100z - 70 - 75 = -44z - 145 \] Right side: \[ 3(5z) - 3(6) + z - 7 = 15z - 18 + z - 7 \] Combine like terms: \[ 15z + z - 18 - 7 = 16z - 25 \] 2. Now, we have: \[ -44z - 145 = 16z - 25 \] 3. Move \(16z\) from the right side to the left side: \[ -44z - 16z - 145 = -25 \] Combine: \[ -60z - 145 = -25 \] 4. Now, add 145 to both sides: \[ -60z = -25 + 145 \] \[ -60z = 120 \] 5. Divide both sides by -60: \[ z = \frac{120}{-60} = -2 \] Thus, the solution is: \[ \boxed{-2} \]