What are the solutions to the equation 12x^3+21x^2+6x=0 ?

The solutions to the equation 12x^3+21x^2+6x=0 are x=0,x=(-7+sqrt(17))/8 ,x=(-7-sqrt(17))/8

Find the zeros of 12x^3+21x^2+6x=0

The zeros of 12x^3+21x^2+6x=0 are x=0,x=(-7+sqrt(17))/8 ,x=(-7-sqrt(17))/8

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12 x^{3} + 21 x^{2} + 6 x = 0

x = 0, x = \frac{- 7 + 17}{8}, x = \frac{- 7 - 17}{8}

Decimal Notation

x = 0, x = - 0.35961 \dots, x = - 1.39038 \dots

Solution steps

12 x^{3} + 21 x^{2} + 6 x = 0

Factor

12 x^{3} + 21 x^{2} + 6 x : 3 x (4 x^{2} + 7 x + 2)

3 x (4 x^{2} + 7 x + 2) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or 4 x^{2} + 7 x + 2 = 0

Solve

4 x^{2} + 7 x + 2 = 0 : x = \frac{- 7 + 17}{8}, x = \frac{- 7 - 17}{8}

The solutions are

x = 0, x = \frac{- 7 + 17}{8}, x = \frac{- 7 - 17}{8}

x^{3} - 7 x^{2} + 17 x - 15 = 0

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

x^{8} = 3^{16}

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

2 h^{4} + 17 h^{3} + 21 h^{2} = h + 7

What are the solutions to the equation 12x^3+21x^2+6x=0 ?
The solutions to the equation 12x^3+21x^2+6x=0 are x=0,x=(-7+sqrt(17))/8 ,x=(-7-sqrt(17))/8
Find the zeros of 12x^3+21x^2+6x=0
The zeros of 12x^3+21x^2+6x=0 are x=0,x=(-7+sqrt(17))/8 ,x=(-7-sqrt(17))/8