What are the solutions to the equation x^3-2x^2+x-1=-x^2+3x-1 ?

The solutions to the equation x^3-2x^2+x-1=-x^2+3x-1 are x=0,x=-1,x=2

Find the zeros of x^3-2x^2+x-1=-x^2+3x-1

The zeros of x^3-2x^2+x-1=-x^2+3x-1 are x=0,x=-1,x=2

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x^{3} - 2 x^{2} + x - 1 = - x^{2} + 3 x - 1

x = 0, x = - 1, x = 2

Solution steps

x^{3} - 2 x^{2} + x - 1 = - x^{2} + 3 x - 1

Move

1

to the right side

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

Move

3 x

to the left side

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

Move

x^{2}

to the left side

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

Factor

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

x (x + 1) (x - 2) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x + 1 = 0 or x - 2 = 0

Solve

x + 1 = 0 : x = - 1

Solve

x - 2 = 0 : x = 2

The solutions are

x = 0, x = - 1, x = 2

30 x^{4} - 30 x^{2} = 0

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

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}

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