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

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

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

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

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

y = - 2, y = - 3, y = 3

Solution steps

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

Move

18

to the left side

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

Move

9 y

to the left side

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

Write in the standard form

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

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

y + 2 = 0 : y = - 2

Solve

y + 3 = 0 : y = - 3

Solve

y - 3 = 0 : y = 3

The solutions are

y = - 2, y = - 3, y = 3

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

x^{4} - 6 x^{3} - 8 x^{2} + 96 x - 128 = 0

10 = 500 (x)^{3}

x^{3} - 6 x^{2} - 15 x - 8 = 0

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

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