What are the solutions to the equation 3x^3=8x^2-4x ?

The solutions to the equation 3x^3=8x^2-4x are x=0,x= 2/3 ,x=2

Find the zeros of 3x^3=8x^2-4x

The zeros of 3x^3=8x^2-4x are x=0,x= 2/3 ,x=2

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3 x^{3} = 8 x^{2} - 4 x

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

Decimal Notation

x = 0, x = 0.66666 \dots, x = 2

Solution steps

3 x^{3} = 8 x^{2} - 4 x

Move

4 x

to the left side

3 x^{3} + 4 x = 8 x^{2}

Move

8 x^{2}

to the left side

3 x^{3} + 4 x - 8 x^{2} = 0

Factor

3 x^{3} + 4 x - 8 x^{2} : x (3 x - 2) (x - 2)

x (3 x - 2) (x - 2) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or 3 x - 2 = 0 or x - 2 = 0

Solve

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

Solve

x - 2 = 0 : x = 2

The solutions are

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

x^{3} + 8 = - 56

12 x^{4} + 11 x^{3} - 26 x^{2} + x + 2 = 0

x, y = (x - 1)^{3}

6 (5 x^{4} - 6 x^{2} + 1) = 0

y^{3} + 0.5 y = 0

What are the solutions to the equation 3x^3=8x^2-4x ?
The solutions to the equation 3x^3=8x^2-4x are x=0,x= 2/3 ,x=2
Find the zeros of 3x^3=8x^2-4x
The zeros of 3x^3=8x^2-4x are x=0,x= 2/3 ,x=2