What are the solutions to the equation y^3+y^2=81y+81 ?

The solutions to the equation y^3+y^2=81y+81 are y=-1,y=-9,y=9

Find the zeros of y^3+y^2=81y+81

The zeros of y^3+y^2=81y+81 are y=-1,y=-9,y=9

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y^{3} + y^{2} = 81 y + 81

y = - 1, y = - 9, y = 9

Solution steps

y^{3} + y^{2} = 81 y + 81

Move

81

to the left side

y^{3} + y^{2} - 81 = 81 y

Move

81 y

to the left side

y^{3} + y^{2} - 81 - 81 y = 0

Write in the standard form

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

y^{3} + y^{2} - 81 y - 81 = 0

Factor

y^{3} + y^{2} - 81 y - 81 : (y + 1) (y + 9) (y - 9)

(y + 1) (y + 9) (y - 9) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

y + 1 = 0 or y + 9 = 0 or y - 9 = 0

Solve

y + 1 = 0 : y = - 1

Solve

y + 9 = 0 : y = - 9

Solve

y - 9 = 0 : y = 9

The solutions are

y = - 1, y = - 9, y = 9

18 q - 21 q^{2} + 6 q^{3} = 0

1 + x^{4} = 0

3 (x + 9) (x^{2} - 81) = 0

x^{3} - 9 x^{2} + 24 x - 16 = 0

2 x^{3} = (x - 1)^{3}

What are the solutions to the equation y^3+y^2=81y+81 ?
The solutions to the equation y^3+y^2=81y+81 are y=-1,y=-9,y=9
Find the zeros of y^3+y^2=81y+81
The zeros of y^3+y^2=81y+81 are y=-1,y=-9,y=9