What are the solutions to the equation 9y^3-6=y-54y^2 ?

The solutions to the equation 9y^3-6=y-54y^2 are y=-6,y=-1/3 ,y= 1/3

Find the zeros of 9y^3-6=y-54y^2

The zeros of 9y^3-6=y-54y^2 are y=-6,y=-1/3 ,y= 1/3

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9 y^{3} - 6 = y - 54 y^{2}

y = - 6, y = - \frac{1}{3}, y = \frac{1}{3}

Decimal Notation

y = - 6, y = - 0.33333 \dots, y = 0.33333 \dots

Solution steps

9 y^{3} - 6 = y - 54 y^{2}

Move

54 y^{2}

to the left side

9 y^{3} - 6 + 54 y^{2} = y

Move

y

to the left side

9 y^{3} - 6 + 54 y^{2} - y = 0

Write in the standard form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

9 y^{3} + 54 y^{2} - y - 6 = 0

Factor

9 y^{3} + 54 y^{2} - y - 6 : (y + 6) (3 y + 1) (3 y - 1)

(y + 6) (3 y + 1) (3 y - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

y + 6 = 0 or 3 y + 1 = 0 or 3 y - 1 = 0

Solve

y + 6 = 0 : y = - 6

Solve

3 y + 1 = 0 : y = - \frac{1}{3}

Solve

3 y - 1 = 0 : y = \frac{1}{3}

The solutions are

y = - 6, y = - \frac{1}{3}, y = \frac{1}{3}

x^{20} = 2

x^{3} + x + 4 = 0

1 + y^{3} = 0

k^{4} - 100 k^{2} = 0

x^{3} - 5 x^{2} + 7 x - 35 = 0

What are the solutions to the equation 9y^3-6=y-54y^2 ?
The solutions to the equation 9y^3-6=y-54y^2 are y=-6,y=-1/3 ,y= 1/3
Find the zeros of 9y^3-6=y-54y^2
The zeros of 9y^3-6=y-54y^2 are y=-6,y=-1/3 ,y= 1/3