Question

2e^(-t)-2te^(-t)=0 solve for t

Answer 1

$2e^{-t}-2te^{-t}=0\\\\2e^{-t}(1-t)=0\iff2e^{-t}=0\ or\ 1-t=0\\\\2e^{-t) > 0\ for\ each\ value\ of\ t\\\\1-t=0\iff t=1$


Answer: t = 1.

Answer 2

$2e^(^-^t^)-2te^(^-^t^)=0$ 

$2e^-^t-2te^-^t=0$     $Simplify \ brackets$ 

$2(\dfrac{1}{e^t}- \dfrac{t}{e^t})=0$    $Factor \ out \ the \ common \ term \ 2$ 

$\dfrac{1}{e^t}- \dfrac{t}{e^t}=0$  $Divide \ both \ sides \ by \ 2$ 

$\dfrac{1-t}{e^t} =0$    $Join \ denominators$ 

$1-t=0$   $Multiply \ both \ sides \ by \ e^t$ 

$-t=-1$   $Subtract \ 1 \ from \ both \ sides$ 

$t=1$    $Multiply \ both \ sides \ by \ -1$