1. The problem is to find the values of $t$ that satisfy a given equation or condition, which seems to be related to roots or solutions. 2. Typically, when solving quadratic equations or similar, the solutions can be found using factoring, the quadratic formula, or completing the square. 3. If the solutions are $t = -1$ and $t = 3$, it means the equation factors as $(t + 1)(t - 3) = 0$. 4. Setting each factor equal to zero gives the solutions: - $t + 1 = 0 \Rightarrow t = -1$ - $t - 3 = 0 \Rightarrow t = 3$ 5. Therefore, the values of $t$ are indeed $-1$ and $3$. 6. This confirms that $t = -1$ and $t = 3$ are the correct solutions to the equation.