What are the solutions to the equation 2+2x-x^2=x^3+3x^2+6x+2 ?

The solutions to the equation 2+2x-x^2=x^3+3x^2+6x+2 are x=0,x=-2

Find the zeros of 2+2x-x^2=x^3+3x^2+6x+2

The zeros of 2+2x-x^2=x^3+3x^2+6x+2 are x=0,x=-2

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2 + 2 x - x^{2} = x^{3} + 3 x^{2} + 6 x + 2

x = 0, x = - 2

Solution steps

2 + 2 x - x^{2} = x^{3} + 3 x^{2} + 6 x + 2

Switch sides

x^{3} + 3 x^{2} + 6 x + 2 = 2 + 2 x - x^{2}

Move

2

to the right side

x^{3} + 3 x^{2} + 6 x = - x^{2} + 2 x

Move

2 x

to the left side

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

Move

x^{2}

to the left side

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

Factor

x^{3} + 4 x^{2} + 4 x : x (x + 2)^{2}

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x + 2 = 0

Solve

x + 2 = 0 : x = - 2

The solutions are

x = 0, x = - 2

s^{3} + 9 s^{2} + 32 s + 32 = 0

(x + 7)^{3} = 0

(s^{2} - 2)^{2} = s^{2}

(x^{3} - 4 x^{2}) - (x - 4) = 0

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

What are the solutions to the equation 2+2x-x^2=x^3+3x^2+6x+2 ?
The solutions to the equation 2+2x-x^2=x^3+3x^2+6x+2 are x=0,x=-2
Find the zeros of 2+2x-x^2=x^3+3x^2+6x+2
The zeros of 2+2x-x^2=x^3+3x^2+6x+2 are x=0,x=-2