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

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

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

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

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

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

Solution steps

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

Move

2

to the left side

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

Move

2 x

to the left side

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x - 2 = 0 : x = 2

Solve

x + 1 = 0 : x = - 1

Solve

x - 1 = 0 : x = 1

The solutions are

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

2^{3} = x^{12}

6 x^{3} + 7 x^{2} - 1 = 0

x^{3} + x^{2} + 2 x + 5 = 0

b x^{3} = 15

x^{5} - 2 x^{4} - 5 x^{3} + 6 x^{2} = 0

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