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

The solutions to the equation 4x^3=x^3+3x^2+2x are x=0,x=(3+sqrt(33))/6 ,x=(3-sqrt(33))/6

Find the zeros of 4x^3=x^3+3x^2+2x

The zeros of 4x^3=x^3+3x^2+2x are x=0,x=(3+sqrt(33))/6 ,x=(3-sqrt(33))/6

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

x = 0, x = \frac{3 + 33}{6}, x = \frac{3 - 33}{6}

Solution steps

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

Switch sides

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

Move

4 x^{3}

to the left side

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

Factor

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

- x (3 x^{2} - 3 x - 2) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or 3 x^{2} - 3 x - 2 = 0

Solve

3 x^{2} - 3 x - 2 = 0 : x = \frac{3 + 33}{6}, x = \frac{3 - 33}{6}

The solutions are

x = 0, x = \frac{3 + 33}{6}, x = \frac{3 - 33}{6}

3 x^{4} - 7 x - 3 x^{2} + 5 x + 2 = 0

x^{4} - 2 x^{3} - 6 x^{2} = 0

1.576 = (1 + x)^{3}

420 = 130 x^{3} + 30

0 = - x^{3} + 4 \cdot x

What are the solutions to the equation 4x^3=x^3+3x^2+2x ?
The solutions to the equation 4x^3=x^3+3x^2+2x are x=0,x=(3+sqrt(33))/6 ,x=(3-sqrt(33))/6
Find the zeros of 4x^3=x^3+3x^2+2x
The zeros of 4x^3=x^3+3x^2+2x are x=0,x=(3+sqrt(33))/6 ,x=(3-sqrt(33))/6