What are the solutions to the equation 24x^3+6x^2-24x=0 ?

The solutions to the equation 24x^3+6x^2-24x=0 are x=0,x=(-1+sqrt(65))/8 ,x=(-1-sqrt(65))/8

Find the zeros of 24x^3+6x^2-24x=0

The zeros of 24x^3+6x^2-24x=0 are x=0,x=(-1+sqrt(65))/8 ,x=(-1-sqrt(65))/8

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24 x^{3} + 6 x^{2} - 24 x = 0

x = 0, x = \frac{- 1 + 65}{8}, x = \frac{- 1 - 65}{8}

Decimal Notation

x = 0, x = 0.88278 \dots, x = - 1.13278 \dots

Solution steps

24 x^{3} + 6 x^{2} - 24 x = 0

Factor

24 x^{3} + 6 x^{2} - 24 x : 6 x (4 x^{2} + x - 4)

6 x (4 x^{2} + x - 4) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

4 x^{2} + x - 4 = 0 : x = \frac{- 1 + 65}{8}, x = \frac{- 1 - 65}{8}

The solutions are

x = 0, x = \frac{- 1 + 65}{8}, x = \frac{- 1 - 65}{8}

x^{4} - 64 x = 0

p^{3} + 2 p + 3 = 0

x^{4} = \frac{16}{9}

x, 729 x^{6} - 4096 = 0

k, k^{3} - 4 k^{2} + k + 6 = 0

What are the solutions to the equation 24x^3+6x^2-24x=0 ?
The solutions to the equation 24x^3+6x^2-24x=0 are x=0,x=(-1+sqrt(65))/8 ,x=(-1-sqrt(65))/8
Find the zeros of 24x^3+6x^2-24x=0
The zeros of 24x^3+6x^2-24x=0 are x=0,x=(-1+sqrt(65))/8 ,x=(-1-sqrt(65))/8