What are the solutions to the equation 12x^3-26x^2-12x=0 ?

The solutions to the equation 12x^3-26x^2-12x=0 are x=0,x=(13+sqrt(313))/(12),x=(13-sqrt(313))/(12)

Find the zeros of 12x^3-26x^2-12x=0

The zeros of 12x^3-26x^2-12x=0 are x=0,x=(13+sqrt(313))/(12),x=(13-sqrt(313))/(12)

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12 x^{3} - 26 x^{2} - 12 x = 0

x = 0, x = \frac{13 + 313}{12}, x = \frac{13 - 313}{12}

Solution steps

12 x^{3} - 26 x^{2} - 12 x = 0

Factor

12 x^{3} - 26 x^{2} - 12 x : 2 x (6 x^{2} - 13 x - 6)

2 x (6 x^{2} - 13 x - 6) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or 6 x^{2} - 13 x - 6 = 0

Solve

6 x^{2} - 13 x - 6 = 0 : x = \frac{13 + 313}{12}, x = \frac{13 - 313}{12}

The solutions are

x = 0, x = \frac{13 + 313}{12}, x = \frac{13 - 313}{12}

25 x^{4} + 9 x^{2} - 16 = 0

x^{6} = 23

x^{6} = 2 x

- a^{3} + 12 a^{2} - 32 a = 0

X^{3} - 3 X^{2} + 20 = 0

What are the solutions to the equation 12x^3-26x^2-12x=0 ?
The solutions to the equation 12x^3-26x^2-12x=0 are x=0,x=(13+sqrt(313))/(12),x=(13-sqrt(313))/(12)
Find the zeros of 12x^3-26x^2-12x=0
The zeros of 12x^3-26x^2-12x=0 are x=0,x=(13+sqrt(313))/(12),x=(13-sqrt(313))/(12)