\(2e^(^-^t^)-2te^(^-^t^)=0\)
\(2e^-^t-2te^-^t=0\) \(Simplify \ brackets\)
\(2(\dfrac{1}{e^t}- \dfrac{t}{e^t})=0\) \(Factor \ out \ the \ common \ term \ 2\)
\(\dfrac{1}{e^t}- \dfrac{t}{e^t}=0\) \(Divide \ both \ sides \ by \ 2\)
\(\dfrac{1-t}{e^t} =0\) \(Join \ denominators\)
\(1-t=0\) \(Multiply \ both \ sides \ by \ e^t\)
\(-t=-1\) \(Subtract \ 1 \ from \ both \ sides\)
\(t=1\) \(Multiply \ both \ sides \ by \ -1\)
