What is the answer to e^{-x}x^4-8e^{-x}x^3+12e^{-x}x^2=0 ?

The answer to e^{-x}x^4-8e^{-x}x^3+12e^{-x}x^2=0 is x=0,x=2,x=6

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e^{-x}x^4-8e^{-x}x^3+12e^{-x}x^2=0

e^{- x} x^{4} - 8 e^{- x} x^{3} + 12 e^{- x} x^{2} = 0

x = 0, x = 2, x = 6

Solution steps

e^{- x} x^{4} - 8 e^{- x} x^{3} + 12 e^{- x} x^{2} = 0

Factor

e^{- x} x^{4} - 8 e^{- x} x^{3} + 12 e^{- x} x^{2} : e^{- x} x^{2} (x - 2) (x - 6)

e^{- x} x^{2} (x - 2) (x - 6) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

e^{- x} = 0 or x = 0 or x - 2 = 0 or x - 6 = 0

Solve

e^{- x} = 0 :

No Solution for

x \in R

Solve

x - 2 = 0 : x = 2

Solve

x - 6 = 0 : x = 6

x = 0, x = 2, x = 6

3^{x} = 5^{2 x}

x, 9^{5 + 2 z} = x

4^{5 x - 2} = 3^{- 2 x + 1}

4 \cdot e^{3 x - 2} = 66

2^{x + 3} = 5^{2 x}

What is the answer to e^{-x}x^4-8e^{-x}x^3+12e^{-x}x^2=0 ?
The answer to e^{-x}x^4-8e^{-x}x^3+12e^{-x}x^2=0 is x=0,x=2,x=6