12(74y - (6+5Y - 8Z) = Please show work
To solve the equation 12(74y - (6+5y - 8z)), we need to simplify the expression within the parentheses first and then distribute the 12.
1. Start with the expression within the innermost parentheses: (6 + 5y - 8z).
Combine like terms: 6 - 8z + 5y = -8z + 5y + 6.
2. Now substitute the simplified expression back into the original equation: 12(74y - (-8z + 5y + 6)).
3. Next, simplify within the parentheses again. Distribute the negative sign to each term within the parentheses:
-12(-8z + 5y + 6) = 96z - 60y - 72.
4. Substitute the simplified expression back into the original equation: 12(74y - (96z - 60y - 72)).
5. Distribute the 12 to each term inside the parentheses:
12(74y - 96z + 60y + 72).
6. Combine like terms and perform any necessary computations:
888y - 1152z + 720y + 864.
7. Combine like terms again:
1608y - 1152z + 864.
Therefore, the simplified expression is 1608y - 1152z + 864.