What are the solutions to the equation 12y^2-13y^3=2y^2-2y ?

The solutions to the equation 12y^2-13y^3=2y^2-2y are y=0,y=(5+sqrt(51))/(13),y=(5-sqrt(51))/(13)

Find the zeros of 12y^2-13y^3=2y^2-2y

The zeros of 12y^2-13y^3=2y^2-2y are y=0,y=(5+sqrt(51))/(13),y=(5-sqrt(51))/(13)

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12 y^{2} - 13 y^{3} = 2 y^{2} - 2 y

y = 0, y = \frac{5 + 51}{13}, y = \frac{5 - 51}{13}

Decimal Notation

y = 0, y = 0.93395 \dots, y = - 0.16472 \dots

Solution steps

12 y^{2} - 13 y^{3} = 2 y^{2} - 2 y

Move

2 y

to the left side

12 y^{2} - 13 y^{3} + 2 y = 2 y^{2}

Move

2 y^{2}

to the left side

- 13 y^{3} + 10 y^{2} + 2 y = 0

Factor

- 13 y^{3} + 10 y^{2} + 2 y : - y (13 y^{2} - 10 y - 2)

- y (13 y^{2} - 10 y - 2) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

y = 0 or 13 y^{2} - 10 y - 2 = 0

Solve

13 y^{2} - 10 y - 2 = 0 : y = \frac{5 + 51}{13}, y = \frac{5 - 51}{13}

The solutions are

y = 0, y = \frac{5 + 51}{13}, y = \frac{5 - 51}{13}

x^{813} = 2

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

16 x^{3} - x = 0

8 k - 48 - 8 k^{8} = k + 15 k

(x (x + 1) (x - 1)) 1 = 2 x - 2

What are the solutions to the equation 12y^2-13y^3=2y^2-2y ?
The solutions to the equation 12y^2-13y^3=2y^2-2y are y=0,y=(5+sqrt(51))/(13),y=(5-sqrt(51))/(13)
Find the zeros of 12y^2-13y^3=2y^2-2y
The zeros of 12y^2-13y^3=2y^2-2y are y=0,y=(5+sqrt(51))/(13),y=(5-sqrt(51))/(13)