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

The answer to xe^{2x}+3ex^2e^{2x}=0 is x=0,x=-1/(3e)

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

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

x = 0, x = - \frac{1}{3 e}

Decimal Notation

x = 0, x = - 0.12262 \dots

Solution steps

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

Factor

x e^{2 x} + 3 e x^{2} e^{2 x} : e^{2 x} x (1 + 3 e x)

e^{2 x} x (1 + 3 e x) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

e^{2 x} = 0 or x = 0 or 1 + 3 e x = 0

Solve

e^{2 x} = 0 :

No Solution for

x \in R

Solve

1 + 3 e x = 0 : x = - \frac{1}{3 e}

x = 0, x = - \frac{1}{3 e}

1.0 5^{t} = 4.35

2^{3 - 2 x} = \frac{1}{8}

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

e^{b} = 46

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

What is the answer to xe^{2x}+3ex^2e^{2x}=0 ?
The answer to xe^{2x}+3ex^2e^{2x}=0 is x=0,x=-1/(3e)