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

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

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

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

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

x = 0, x = \frac{1}{2} + i \frac{3}{2}, x = \frac{1}{2} - i \frac{3}{2}

Solution steps

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

Move

x

to the left side

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

Factor

x^{3} - x^{2} + x : x (x^{2} - x + 1)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x^{2} - x + 1 = 0

Solve

x^{2} - x + 1 = 0 : x = \frac{1}{2} + i \frac{3}{2}, x = \frac{1}{2} - i \frac{3}{2}

The solutions are

x = 0, x = \frac{1}{2} + i \frac{3}{2}, x = \frac{1}{2} - i \frac{3}{2}

2 x^{3} + 5 x^{2} - 8 x - 20 = 0

6 x - 5 x^{2} - x^{3} = 0

(x + 1)^{2} - 3 x (x + 1)^{2} = 0

3 a^{4} + 2 a - 46 = 54

- 2 x^{4} + 9 = 2 x - 1

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