What are the solutions to the equation n^3-n=5n^2-5 ?

The solutions to the equation n^3-n=5n^2-5 are n=5,n=-1,n=1

Find the zeros of n^3-n=5n^2-5

The zeros of n^3-n=5n^2-5 are n=5,n=-1,n=1

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n^{3} - n = 5 n^{2} - 5

n = 5, n = - 1, n = 1

Solution steps

n^{3} - n = 5 n^{2} - 5

Move

5

to the left side

n^{3} - n + 5 = 5 n^{2}

Move

5 n^{2}

to the left side

n^{3} - n + 5 - 5 n^{2} = 0

Write in the standard form

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

n^{3} - 5 n^{2} - n + 5 = 0

Factor

n^{3} - 5 n^{2} - n + 5 : (n - 5) (n + 1) (n - 1)

(n - 5) (n + 1) (n - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

n - 5 = 0 or n + 1 = 0 or n - 1 = 0

Solve

n - 5 = 0 : n = 5

Solve

n + 1 = 0 : n = - 1

Solve

n - 1 = 0 : n = 1

The solutions are

n = 5, n = - 1, n = 1

x^{3} - 8 = 0

x^{10000} = 12

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

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

y, 4 x y^{4} - x^{3} = y^{2} + 5

What are the solutions to the equation n^3-n=5n^2-5 ?
The solutions to the equation n^3-n=5n^2-5 are n=5,n=-1,n=1
Find the zeros of n^3-n=5n^2-5
The zeros of n^3-n=5n^2-5 are n=5,n=-1,n=1