What is the answer to 6e^{-x}x^5-e^{-x}x^6=0 ?

The answer to 6e^{-x}x^5-e^{-x}x^6=0 is x=0,x=6

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6e^{-x}x^5-e^{-x}x^6=0

6 e^{- x} x^{5} - e^{- x} x^{6} = 0

x = 0, x = 6

Solution steps

6 e^{- x} x^{5} - e^{- x} x^{6} = 0

Factor

6 e^{- x} x^{5} - e^{- x} x^{6} : e^{- x} x^{5} (6 - x)

e^{- x} x^{5} (6 - x) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

e^{- x} = 0 or x = 0 or 6 - x = 0

Solve

e^{- x} = 0 :

No Solution for

x \in R

Solve

6 - x = 0 : x = 6

x = 0, x = 6

500 e^{- x} = 300

4^{2 x} = (\frac{1}{2})^{x + 5}

9^{x} = 2

10 e^{16 x} = 16

What is the answer to 6e^{-x}x^5-e^{-x}x^6=0 ?
The answer to 6e^{-x}x^5-e^{-x}x^6=0 is x=0,x=6