What are the solutions to the equation 5x^3-2(x^3+x)=-x ?

The solutions to the equation 5x^3-2(x^3+x)=-x are x=0,x=-1/(sqrt(3)),x= 1/(sqrt(3))

Find the zeros of 5x^3-2(x^3+x)=-x

The zeros of 5x^3-2(x^3+x)=-x are x=0,x=-1/(sqrt(3)),x= 1/(sqrt(3))

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5 x^{3} - 2 (x^{3} + x) = - x

x = 0, x = - \frac{1}{3}, x = \frac{1}{3}

Decimal Notation

x = 0, x = - 0.57735 \dots, x = 0.57735 \dots

Solution steps

5 x^{3} - 2 (x^{3} + x) = - x

Expand

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

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

Move

x

to the left side

3 x^{3} - x = 0

Factor

3 x^{3} - x : x (3 x + 1) (3 x - 1)

x (3 x + 1) (3 x - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or 3 x + 1 = 0 or 3 x - 1 = 0

Solve

3 x + 1 = 0 : x = - \frac{1}{3}

Solve

3 x - 1 = 0 : x = \frac{1}{3}

The solutions are

x = 0, x = - \frac{1}{3}, x = \frac{1}{3}

2 x^{4} - 16 x^{3} + 32 x^{2} + 5 = 0

5 x^{16} = 10 x + 15

21 x^{4} = 119 x^{2} - 1

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

9 x^{3} = x

What are the solutions to the equation 5x^3-2(x^3+x)=-x ?
The solutions to the equation 5x^3-2(x^3+x)=-x are x=0,x=-1/(sqrt(3)),x= 1/(sqrt(3))
Find the zeros of 5x^3-2(x^3+x)=-x
The zeros of 5x^3-2(x^3+x)=-x are x=0,x=-1/(sqrt(3)),x= 1/(sqrt(3))