Solve the quadratic equation by factoring. \[ t^{2}+7 t+4=t-5 \]

First, let's rearrange the equation to set it to zero: \[ t^2 + 7t + 4 - t + 5 = 0 \] This simplifies to: \[ t^2 + 6t + 9 = 0 \] Next, we can factor the quadratic: \[ (t + 3)(t + 3) = 0 \] or \[ (t + 3)^2 = 0 \] Setting the factor equal to zero gives us: \[ t + 3 = 0 \] So, the solution is: \[ t = -3 \] The quadratic has one solution, a double root at \( t = -3 \).