What is the answer to x^2e^{-3x}=e^{-3x}(2x+15) ?

The answer to x^2e^{-3x}=e^{-3x}(2x+15) is x=-3,x=5

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x^2e^{-3x}=e^{-3x}(2x+15)

x^{2} e^{- 3 x} = e^{- 3 x} (2 x + 15)

x = - 3, x = 5

Solution steps

x^{2} e^{- 3 x} = e^{- 3 x} (2 x + 15)

Subtract

e^{- 3 x} (2 x + 15)

from both sides

x^{2} e^{- 3 x} - e^{- 3 x} (2 x + 15) = e^{- 3 x} (2 x + 15) - e^{- 3 x} (2 x + 15)

Simplify

x^{2} e^{- 3 x} - e^{- 3 x} (2 x + 15) = 0

Factor

x^{2} e^{- 3 x} - e^{- 3 x} (2 x + 15) : e^{- 3 x} (x + 3) (x - 5)

e^{- 3 x} (x + 3) (x - 5) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

e^{- 3 x} = 0 or x + 3 = 0 or x - 5 = 0

Solve

e^{- 3 x} = 0 :

No Solution for

x \in R

Solve

x + 3 = 0 : x = - 3

Solve

x - 5 = 0 : x = 5

x = - 3, x = 5

5 \cdot 2 5^{x + 1} = 12 5^{2 x}

2^{- x - 7} = 1 1^{2 x}

1 6^{x + 4} = 6 4^{4 x - 2}

5^{3 x + 2} = 25

2^{x - 1} = 2^{2 x + 8}

What is the answer to x^2e^{-3x}=e^{-3x}(2x+15) ?
The answer to x^2e^{-3x}=e^{-3x}(2x+15) is x=-3,x=5