What is the answer to 3x^3e^{-4x}-10x^2e^{-4x}=48xe^{-4x} ?

The answer to 3x^3e^{-4x}-10x^2e^{-4x}=48xe^{-4x} is x=0,x=-8/3 ,x=6

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3x^3e^{-4x}-10x^2e^{-4x}=48xe^{-4x}

3 x^{3} e^{- 4 x} - 10 x^{2} e^{- 4 x} = 48 x e^{- 4 x}

x = 0, x = - \frac{8}{3}, x = 6

Decimal Notation

x = 0, x = - 2.66666 \dots, x = 6

Solution steps

3 x^{3} e^{- 4 x} - 10 x^{2} e^{- 4 x} = 48 x e^{- 4 x}

Subtract

48 x e^{- 4 x}

from both sides

3 x^{3} e^{- 4 x} - 10 x^{2} e^{- 4 x} - 48 x e^{- 4 x} = 48 x e^{- 4 x} - 48 x e^{- 4 x}

Simplify

3 x^{3} e^{- 4 x} - 10 x^{2} e^{- 4 x} - 48 x e^{- 4 x} = 0

Factor

3 x^{3} e^{- 4 x} - 10 x^{2} e^{- 4 x} - 48 x e^{- 4 x} : e^{- 4 x} x (3 x + 8) (x - 6)

e^{- 4 x} x (3 x + 8) (x - 6) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

e^{- 4 x} = 0 or x = 0 or 3 x + 8 = 0 or x - 6 = 0

Solve

e^{- 4 x} = 0 :

No Solution for

x \in R

Solve

3 x + 8 = 0 : x = - \frac{8}{3}

Solve

x - 6 = 0 : x = 6

x = 0, x = - \frac{8}{3}, x = 6

3^{k} = 33

10 0^{x - 2} = 100 0^{x}

\frac{8 1 ^{x + 5}}{3 ^{7 x + 2}} = 3^{x - 2}

4 \times 5^{x + 1} - 5 = 35

What is the answer to 3x^3e^{-4x}-10x^2e^{-4x}=48xe^{-4x} ?
The answer to 3x^3e^{-4x}-10x^2e^{-4x}=48xe^{-4x} is x=0,x=-8/3 ,x=6