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

The solutions to the equation x^3+2x^2+3x=-6 are x=-2,x=sqrt(3)i,x=-sqrt(3)i

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

The zeros of x^3+2x^2+3x=-6 are x=-2,x=sqrt(3)i,x=-sqrt(3)i

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

x = - 2, x = 3 i, x = - 3 i

Solution steps

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

Move

6

to the left side

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

Factor

x^{3} + 2 x^{2} + 3 x + 6 : (x + 2) (x^{2} + 3)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x + 2 = 0 : x = - 2

Solve

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

The solutions are

x = - 2, x = 3 i, x = - 3 i

3 x^{3} - 25 x^{2} + 58 x - 40 = 0

x^{4} + 8 x^{3} + 8 x^{2} + 8 x + 7 = 0

x^{3} - 9 x^{2} - 4 x + 36 = 0

x^{12} - x^{6} - 30 = 0

240 x^{3} + 360 x^{2} - 1800 x = 0

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