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

The solutions to the equation n^3-n=9n^2-9 are n=9,n=-1,n=1

Find the zeros of n^3-n=9n^2-9

The zeros of n^3-n=9n^2-9 are n=9,n=-1,n=1

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n^{3} - n = 9 n^{2} - 9

n = 9, n = - 1, n = 1

Solution steps

n^{3} - n = 9 n^{2} - 9

Move

9

to the left side

n^{3} - n + 9 = 9 n^{2}

Move

9 n^{2}

to the left side

n^{3} - n + 9 - 9 n^{2} = 0

Write in the standard form

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

n^{3} - 9 n^{2} - n + 9 = 0

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

n - 9 = 0 or n + 1 = 0 or n - 1 = 0

Solve

n - 9 = 0 : n = 9

Solve

n + 1 = 0 : n = - 1

Solve

n - 1 = 0 : n = 1

The solutions are

n = 9, n = - 1, n = 1

x^{3} - 6 x^{2} + 5 x - 1 = 0

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

y, 12 y^{3} - 1 y^{2} - 6 y = 0

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

r^{3} + r = 0

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