What are the solutions to the equation 12x^3+27x^2-30x=0 ?

The solutions to the equation 12x^3+27x^2-30x=0 are x=0,x=(-9+sqrt(241))/8 ,x=(-9-sqrt(241))/8

Find the zeros of 12x^3+27x^2-30x=0

The zeros of 12x^3+27x^2-30x=0 are x=0,x=(-9+sqrt(241))/8 ,x=(-9-sqrt(241))/8

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12 x^{3} + 27 x^{2} - 30 x = 0

x = 0, x = \frac{- 9 + 241}{8}, x = \frac{- 9 - 241}{8}

Decimal Notation

x = 0, x = 0.81552 \dots, x = - 3.06552 \dots

Solution steps

12 x^{3} + 27 x^{2} - 30 x = 0

Factor

12 x^{3} + 27 x^{2} - 30 x : 3 x (4 x^{2} + 9 x - 10)

3 x (4 x^{2} + 9 x - 10) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or 4 x^{2} + 9 x - 10 = 0

Solve

4 x^{2} + 9 x - 10 = 0 : x = \frac{- 9 + 241}{8}, x = \frac{- 9 - 241}{8}

The solutions are

x = 0, x = \frac{- 9 + 241}{8}, x = \frac{- 9 - 241}{8}

(1 - x^{2})^{2} = 0

4 x^{3} + 6 x = 0

x^{3} = - 343

2 x^{3} + 6 x^{2} + 1 = 0

6 x^{3} - 47 x^{2} + 36 x - 7 = 0

What are the solutions to the equation 12x^3+27x^2-30x=0 ?
The solutions to the equation 12x^3+27x^2-30x=0 are x=0,x=(-9+sqrt(241))/8 ,x=(-9-sqrt(241))/8
Find the zeros of 12x^3+27x^2-30x=0
The zeros of 12x^3+27x^2-30x=0 are x=0,x=(-9+sqrt(241))/8 ,x=(-9-sqrt(241))/8