What are the solutions to the equation 3x^3+2x^2=12x+8 ?

The solutions to the equation 3x^3+2x^2=12x+8 are x=-2/3 ,x=-2,x=2

Find the zeros of 3x^3+2x^2=12x+8

The zeros of 3x^3+2x^2=12x+8 are x=-2/3 ,x=-2,x=2

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3 x^{3} + 2 x^{2} = 12 x + 8

x = - \frac{2}{3}, x = - 2, x = 2

Decimal Notation

x = - 0.66666 \dots, x = - 2, x = 2

Solution steps

3 x^{3} + 2 x^{2} = 12 x + 8

Move

8

to the left side

3 x^{3} + 2 x^{2} - 8 = 12 x

Move

12 x

to the left side

3 x^{3} + 2 x^{2} - 8 - 12 x = 0

Write in the standard form

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

3 x^{3} + 2 x^{2} - 12 x - 8 = 0

Factor

3 x^{3} + 2 x^{2} - 12 x - 8 : (3 x + 2) (x + 2) (x - 2)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

3 x + 2 = 0 : x = - \frac{2}{3}

Solve

x + 2 = 0 : x = - 2

Solve

x - 2 = 0 : x = 2

The solutions are

x = - \frac{2}{3}, x = - 2, x = 2

x^{3} = 17

x^{3} + 3 x^{2} + 5 x + 15 = 0

x^{4} - 4 x^{2} + 1 = 0

x^{3} - 8 x^{2} + 21 x - 18 = 0

x^{3} + 3 x^{2} = 36 x + 108

What are the solutions to the equation 3x^3+2x^2=12x+8 ?
The solutions to the equation 3x^3+2x^2=12x+8 are x=-2/3 ,x=-2,x=2
Find the zeros of 3x^3+2x^2=12x+8
The zeros of 3x^3+2x^2=12x+8 are x=-2/3 ,x=-2,x=2