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To solve this problem, we will distribute and combine like terms.
First, distribute the first term:
12(z + 4) - 3(14z + 1) = 12z + 48 - 42z - 3
Now, combine like terms:
12z - 42z + 48 - 3 = (12z - 42z) + (48 - 3) = -30z + 45
Therefore, the simplified expression is -30z + 45.