What is the answer to 8x^3e^{-2x}-2x^42e^{-2x}=0 ?

The answer to 8x^3e^{-2x}-2x^42e^{-2x}=0 is x=0,x=2

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8x^3e^{-2x}-2x^42e^{-2x}=0

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

x = 0, x = 2

Solution steps

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

Factor

8 x^{3} e^{- 2 x} - 2 x^{4} \cdot 2 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

e^{2 x + 1} = 7

2 x = 2^{- x}

\frac{4 ^{4 x}}{4 ^{x + 2}} = 16

3^{x + 1} = 2^{x - 1}

4^{m + 1} = \frac{1}{8 2}

What is the answer to 8x^3e^{-2x}-2x^42e^{-2x}=0 ?
The answer to 8x^3e^{-2x}-2x^42e^{-2x}=0 is x=0,x=2