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

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

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

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

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

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

Solution steps

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

Move

2

to the left side

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

Move

x

to the left side

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

Write in the standard form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

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

x^{3} - 10 x^{2} + 28 x + 24 = 0

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

12 x^{2} - 4 x^{2} = x^{3}

20 y^{4} + 160 y^{2} - 285 = 0

27000 = 20000 \cdot (1 + x)^{6}

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