Factor. \[ 7 z^{2}-4 z-3 \]

Step 1 ：The given expression is a quadratic equation in the form of \(ax^2 + bx + c\).

Step 2 ：To factorize it, we need to find two numbers such that their sum is equal to the coefficient of the middle term (which is -4 in this case) and their product is equal to the product of the coefficient of the first term (which is 7 in this case) and the last term (which is -3 in this case).

Step 3 ：The factored form of the given expression is \((z - 1)(7z + 3)\)

Step 4 ：\(\boxed{(z - 1)(7z + 3)}\) is the final answer.