What is the answer to 5x^3e^x=2xe^x ?

The answer to 5x^3e^x=2xe^x is x=0,x=-sqrt(2/5),x=sqrt(2/5)

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5x^3e^x=2xe^x

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

x = 0, x = - \frac{2}{5}, x = \frac{2}{5}

Decimal Notation

x = 0, x = - 0.63245 \dots, x = 0.63245 \dots

Solution steps

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

Subtract

2 x e^{x}

from both sides

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

Simplify

5 x^{3} e^{x} - 2 x e^{x} = 0

Factor

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

e^{x} x (5 x + 2) (5 x - 2) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

e^{x} = 0 or x = 0 or 5 x + 2 = 0 or 5 x - 2 = 0

Solve

e^{x} = 0 :

No Solution for

x \in R

Solve

5 x + 2 = 0 : x = - \frac{2}{5}

Solve

5 x - 2 = 0 : x = \frac{2}{5}

x = 0, x = - \frac{2}{5}, x = \frac{2}{5}

2^{8 x + 5} = 8^{x^{2} - 2}

e^{x} e^{x + 1} = 10

4 9^{x} - 7^{x + 1} = 8

4 9^{5 x + 2} = (\frac{1}{7})^{11 - x}

e^{x^{2}} = 1

What is the answer to 5x^3e^x=2xe^x ?
The answer to 5x^3e^x=2xe^x is x=0,x=-sqrt(2/5),x=sqrt(2/5)