What are the solutions to the equation y^3-27=9y^2-27y ?

The solutions to the equation y^3-27=9y^2-27y are y=3

Find the zeros of y^3-27=9y^2-27y

The zeros of y^3-27=9y^2-27y are y=3

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y^{3} - 27 = 9 y^{2} - 27 y

y = 3

Solution steps

y^{3} - 27 = 9 y^{2} - 27 y

Move

27 y

to the left side

y^{3} - 27 + 27 y = 9 y^{2}

Move

9 y^{2}

to the left side

y^{3} - 27 + 27 y - 9 y^{2} = 0

Write in the standard form

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

y^{3} - 9 y^{2} + 27 y - 27 = 0

Factor

y^{3} - 9 y^{2} + 27 y - 27 : (y - 3)^{3}

(y - 3)^{3} = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

y - 3 = 0

Solve

y - 3 = 0 : y = 3

The solution is

y = 3

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

x^{3} - 13 x - 12 = 0

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

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

4 c^{3} + 4 c^{2} - 48 c = 0

What are the solutions to the equation y^3-27=9y^2-27y ?
The solutions to the equation y^3-27=9y^2-27y are y=3
Find the zeros of y^3-27=9y^2-27y
The zeros of y^3-27=9y^2-27y are y=3