What is the answer to 3x^2e^{-x}-x^3e^{-x}=0 ?

The answer to 3x^2e^{-x}-x^3e^{-x}=0 is x=0,x=3

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3x^2e^{-x}-x^3e^{-x}=0

3 x^{2} e^{- x} - x^{3} e^{- x} = 0

x = 0, x = 3

Solution steps

3 x^{2} e^{- x} - x^{3} e^{- x} = 0

Factor

3 x^{2} e^{- x} - x^{3} e^{- x} : e^{- x} x^{2} (3 - x)

e^{- x} x^{2} (3 - x) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

e^{- x} = 0 or x = 0 or 3 - x = 0

Solve

e^{- x} = 0 :

No Solution for

x \in R

Solve

3 - x = 0 : x = 3

x = 0, x = 3

7^{x + 1} = 1

7^{x - 2} = 3^{2 - x}

3^{x + 5} = 4

3^{x + 2} - 3^{x} = 216

7^{- 3 - x} = 242

What is the answer to 3x^2e^{-x}-x^3e^{-x}=0 ?
The answer to 3x^2e^{-x}-x^3e^{-x}=0 is x=0,x=3