n(n+5)(n-8)=0

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Solution for n(n+5)(n-8)=0 equation: 


Simplifying
n(n + 5)(n + -8) = 0

Reorder the terms:
n(5 + n)(n + -8) = 0

Reorder the terms:
n(5 + n)(-8 + n) = 0

Multiply (5 + n) * (-8 + n)
n(5(-8 + n) + n(-8 + n)) = 0
n((-8 * 5 + n * 5) + n(-8 + n)) = 0
n((-40 + 5n) + n(-8 + n)) = 0
n(-40 + 5n + (-8 * n + n * n)) = 0
n(-40 + 5n + (-8n + n2)) = 0

Combine like terms: 5n + -8n = -3n
n(-40 + -3n + n2) = 0
(-40 * n + -3n * n + n2 * n) = 0
(-40n + -3n2 + n3) = 0

Solving
-40n + -3n2 + n3 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), 'n'.
n(-40 + -3n + n2) = 0

Factor a trinomial.
n((-5 + -1n)(8 + -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 '(8 + -1n)' equal to zero and attempt to solve:

Simplifying
8 + -1n = 0

Solving
8 + -1n = 0

Move all terms containing n to the left, all other terms to the right.

Add '-8' to each side of the equation.
8 + -8 + -1n = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1n = 0 + -8
-1n = 0 + -8

Combine like terms: 0 + -8 = -8
-1n = -8

Divide each side by '-1'.
n = 8

Simplifying
n = 8
Solution
n = {0, -5, 8}

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