What are the solutions to the equation 9y^3+8=4y+18y^2 ?

The solutions to the equation 9y^3+8=4y+18y^2 are y=2,y=-2/3 ,y= 2/3

Find the zeros of 9y^3+8=4y+18y^2

The zeros of 9y^3+8=4y+18y^2 are y=2,y=-2/3 ,y= 2/3

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9 y^{3} + 8 = 4 y + 18 y^{2}

y = 2, y = - \frac{2}{3}, y = \frac{2}{3}

Decimal Notation

y = 2, y = - 0.66666 \dots, y = 0.66666 \dots

Solution steps

9 y^{3} + 8 = 4 y + 18 y^{2}

Move

18 y^{2}

to the left side

9 y^{3} + 8 - 18 y^{2} = 4 y

Move

4 y

to the left side

9 y^{3} + 8 - 18 y^{2} - 4 y = 0

Write in the standard form

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

9 y^{3} - 18 y^{2} - 4 y + 8 = 0

Factor

9 y^{3} - 18 y^{2} - 4 y + 8 : (y - 2) (3 y + 2) (3 y - 2)

(y - 2) (3 y + 2) (3 y - 2) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

y - 2 = 0 or 3 y + 2 = 0 or 3 y - 2 = 0

Solve

y - 2 = 0 : y = 2

Solve

3 y + 2 = 0 : y = - \frac{2}{3}

Solve

3 y - 2 = 0 : y = \frac{2}{3}

The solutions are

y = 2, y = - \frac{2}{3}, y = \frac{2}{3}

2 - 15 x + 9 x^{2} - x^{3} = 0

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

x (9 + x) (x - 2) = 4

x^{4} - 5 x^{2} - 10 x - 6 = 0

100 x^{3} - 45 x^{2} - 58 x + 24 = 0

What are the solutions to the equation 9y^3+8=4y+18y^2 ?
The solutions to the equation 9y^3+8=4y+18y^2 are y=2,y=-2/3 ,y= 2/3
Find the zeros of 9y^3+8=4y+18y^2
The zeros of 9y^3+8=4y+18y^2 are y=2,y=-2/3 ,y= 2/3