What is the answer to -x^2e^{-x}+2xe^{-x}=0 ?

The answer to -x^2e^{-x}+2xe^{-x}=0 is x=0,x=2

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-x^2e^{-x}+2xe^{-x}=0

- x^{2} e^{- x} + 2 x e^{- x} = 0

x = 0, x = 2

Solution steps

- x^{2} e^{- x} + 2 x e^{- x} = 0

Factor

- x^{2} e^{- x} + 2 x e^{- x} : e^{- x} x (- x + 2)

e^{- x} x (- x + 2) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

e^{- x} = 0 or x = 0 or - x + 2 = 0

Solve

e^{- x} = 0 :

No Solution for

x \in R

Solve

- x + 2 = 0 : x = 2

x = 0, x = 2

2^{\frac{x}{2}} + 2^{x} = 6

7^{3 x + 1} = e^{x}

3^{x} = 93

4^{2 x + 1} = 1024

What is the answer to -x^2e^{-x}+2xe^{-x}=0 ?
The answer to -x^2e^{-x}+2xe^{-x}=0 is x=0,x=2