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

The solutions to the equation 12y^2-12y^3=2y^2-2y are y=0,y=-1/6 ,y=1

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

The zeros of 12y^2-12y^3=2y^2-2y are y=0,y=-1/6 ,y=1

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

y = 0, y = - \frac{1}{6}, y = 1

Decimal Notation

y = 0, y = - 0.16666 \dots, y = 1

Solution steps

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

Move

2 y

to the left side

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

Move

2 y^{2}

to the left side

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

Factor

- 12 y^{3} + 10 y^{2} + 2 y : - 2 y (6 y + 1) (y - 1)

- 2 y (6 y + 1) (y - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

y = 0 or 6 y + 1 = 0 or y - 1 = 0

Solve

6 y + 1 = 0 : y = - \frac{1}{6}

Solve

y - 1 = 0 : y = 1

The solutions are

y = 0, y = - \frac{1}{6}, y = 1

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

6 x^{4} - x^{2} - 1 = 0

0 = x^{3} - 13

z^{6} + 1 = 3 i

x^{4} + 2 x^{3} - 4 x^{2} - 5 x - 6 = 0

What are the solutions to the equation 12y^2-12y^3=2y^2-2y ?
The solutions to the equation 12y^2-12y^3=2y^2-2y are y=0,y=-1/6 ,y=1
Find the zeros of 12y^2-12y^3=2y^2-2y
The zeros of 12y^2-12y^3=2y^2-2y are y=0,y=-1/6 ,y=1