What is the answer to 3x^2e^{3x}+2xe^{3x}=0 ?

The answer to 3x^2e^{3x}+2xe^{3x}=0 is x=0,x=-2/3

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3x^2e^{3x}+2xe^{3x}=0

3 x^{2} e^{3 x} + 2 x e^{3 x} = 0

x = 0, x = - \frac{2}{3}

Solution steps

3 x^{2} e^{3 x} + 2 x e^{3 x} = 0

Factor

3 x^{2} e^{3 x} + 2 x e^{3 x} : e^{3 x} x (3 x + 2)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

e^{3 x} = 0 or x = 0 or 3 x + 2 = 0

Solve

e^{3 x} = 0 :

No Solution for

x \in R

Solve

3 x + 2 = 0 : x = - \frac{2}{3}

x = 0, x = - \frac{2}{3}

2^{2 x} - 10 (2^{x}) + 16 = 0

e^{x} + e^{- x} = 4

30 = 1 0^{x}

64 \cdot 1 6^{- 3 x} = 1 6^{3 x - 2}

12 5^{2 - 3 x} = 5

What is the answer to 3x^2e^{3x}+2xe^{3x}=0 ?
The answer to 3x^2e^{3x}+2xe^{3x}=0 is x=0,x=-2/3