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),x=sqrt(3)

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),x=sqrt(3)

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

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

Decimal Notation

x = - 2, x = - 1.73205 \dots, x = 1.73205 \dots

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 + 3) (x - 3)

(x + 2) (x + 3) (x - 3) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 2 = 0 or x + 3 = 0 or x - 3 = 0

Solve

x + 2 = 0 : x = - 2

Solve

x + 3 = 0 : x = - 3

Solve

x - 3 = 0 : x = 3

The solutions are

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

x^{3} - 5 x^{2} + 4 x = x (x - 4)

x^{2} = x^{5}

36 x^{4} + 9 = 45 x^{2}

2 x^{3} - 10 x^{2} - 12 x = 0

4 x^{3} = 68

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),x=sqrt(3)
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),x=sqrt(3)