What are the solutions to the equation y^3+y^2=36y+36 ?

The solutions to the equation y^3+y^2=36y+36 are y=-1,y=-6,y=6

Find the zeros of y^3+y^2=36y+36

The zeros of y^3+y^2=36y+36 are y=-1,y=-6,y=6

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y^{3} + y^{2} = 36 y + 36

y = - 1, y = - 6, y = 6

Solution steps

y^{3} + y^{2} = 36 y + 36

Move

36

to the left side

y^{3} + y^{2} - 36 = 36 y

Move

36 y

to the left side

y^{3} + y^{2} - 36 - 36 y = 0

Write in the standard form

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

y^{3} + y^{2} - 36 y - 36 = 0

Factor

y^{3} + y^{2} - 36 y - 36 : (y + 1) (y + 6) (y - 6)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

y + 1 = 0 : y = - 1

Solve

y + 6 = 0 : y = - 6

Solve

y - 6 = 0 : y = 6

The solutions are

y = - 1, y = - 6, y = 6

1031 = x^{5} + x + 3

2 x^{4} - 3 x^{2} + 1 = 0

x, 0 = x^{3} - y + 5

2 x^{3} - 5 x^{2} = 12 x

n^{3} = 8

What are the solutions to the equation y^3+y^2=36y+36 ?
The solutions to the equation y^3+y^2=36y+36 are y=-1,y=-6,y=6
Find the zeros of y^3+y^2=36y+36
The zeros of y^3+y^2=36y+36 are y=-1,y=-6,y=6