What is the answer to 8x^3e^{-2x}-4x^4e^{-2x}=0 ?

The answer to 8x^3e^{-2x}-4x^4e^{-2x}=0 is x=0,x=2

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8x^3e^{-2x}-4x^4e^{-2x}=0

8 x^{3} e^{- 2 x} - 4 x^{4} e^{- 2 x} = 0

x = 0, x = 2

Solution steps

8 x^{3} e^{- 2 x} - 4 x^{4} e^{- 2 x} = 0

Factor

8 x^{3} e^{- 2 x} - 4 x^{4} e^{- 2 x} : 4 e^{- 2 x} x^{3} (2 - x)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

e^{- 2 x} = 0 :

No Solution for

x \in R

Solve

2 - x = 0 : x = 2

x = 0, x = 2

9^{x - 2} = 27

3^{1 - x} = 243

x, e^{x y} x = 0

15.48 = 16 + 54 e^{- k (30)}

5^{2 x - 3} = 1255

What is the answer to 8x^3e^{-2x}-4x^4e^{-2x}=0 ?
The answer to 8x^3e^{-2x}-4x^4e^{-2x}=0 is x=0,x=2