What is the answer to 3e^{3x}(10-6x)+e^{3x}(-6)=0 ?

The answer to 3e^{3x}(10-6x)+e^{3x}(-6)=0 is x= 4/3

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3e^{3x}(10-6x)+e^{3x}(-6)=0

3 e^{3 x} (10 - 6 x) + e^{3 x} (- 6) = 0

x = \frac{4}{3}

Decimal Notation

x = 1.33333 \dots

Solution steps

3 e^{3 x} (10 - 6 x) + e^{3 x} (- 6) = 0

Factor

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

e^{3 x} = 0 or 3 x - 4 = 0

Solve

e^{3 x} = 0 :

No Solution for

x \in R

Solve

3 x - 4 = 0 : x = \frac{4}{3}

x = \frac{4}{3}

e^{- x^{3}} = \frac{1}{e ^{x^{3}}}

8^{a} = 23

t, e^{- 0.2 t} = 4

3^{3 x - 2} = 1

2^{x + 1} = 8192

What is the answer to 3e^{3x}(10-6x)+e^{3x}(-6)=0 ?
The answer to 3e^{3x}(10-6x)+e^{3x}(-6)=0 is x= 4/3