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

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Solution for n(n+5)(n-1)=0 equation:


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

Reorder the terms:
n(5 + n)(n + -1) = 0

Reorder the terms:
n(5 + n)(-1 + n) = 0

Multiply (5 + n) * (-1 + n)
n(5(-1 + n) + n(-1 + n)) = 0
n((-1 * 5 + n * 5) + n(-1 + n)) = 0
n((-5 + 5n) + n(-1 + n)) = 0
n(-5 + 5n + (-1 * n + n * n)) = 0
n(-5 + 5n + (-1n + n2)) = 0

Combine like terms: 5n + -1n = 4n
n(-5 + 4n + n2) = 0
(-5 * n + 4n * n + n2 * n) = 0
(-5n + 4n2 + n3) = 0

Solving
-5n + 4n2 + n3 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), 'n'.
n(-5 + 4n + n2) = 0

Factor a trinomial.
n((-5 + -1n)(1 + -1n)) = 0

Subproblem 1

Set the factor 'n' equal to zero and attempt to solve: Simplifying n = 0 Solving n = 0 Move all terms containing n to the left, all other terms to the right. Simplifying n = 0

Subproblem 2

Set the factor '(-5 + -1n)' equal to zero and attempt to solve: Simplifying -5 + -1n = 0 Solving -5 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1n = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1n = 0 + 5 -1n = 0 + 5 Combine like terms: 0 + 5 = 5 -1n = 5 Divide each side by '-1'. n = -5 Simplifying n = -5

Subproblem 3

Set the factor '(1 + -1n)' equal to zero and attempt to solve: Simplifying 1 + -1n = 0 Solving 1 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1n = 0 + -1 -1n = 0 + -1 Combine like terms: 0 + -1 = -1 -1n = -1 Divide each side by '-1'. n = 1 Simplifying n = 1

Solution

n = {0, -5, 1}

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