Step 1 :The expression on the right of the equal sign is a quadratic equation in the form of \(ax(bx+c)(dx-e)\) where a, b, c, d, and e are constants and x is the variable. In this case, a = 16, b = 1, c = 2, d = -1, and e = 22.
Step 2 :The values for t that will make the expression have a value of 0 are the roots of the equation. In a multiplication operation, the result can be 0 if any of the factors is 0. Therefore, we need to find the values of t that make either \((2+t)\) or \((22-t)\) equal to 0.
Step 3 :The roots of the equation are -2 and 22. These are the values for t that will make the expression \(16(2+t)(22-t)\) equal to 0.
Step 4 :Final Answer: The values for t that will make the expression \(16(2+t)(22-t)\) have a value of 0 are \(\boxed{-2}\) and \(\boxed{22}\).