5n(n-3)(n-4)=0

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Solution for 5n(n-3)(n-4)=0 equation: 


Simplifying
5n(n + -3)(n + -4) = 0

Reorder the terms:
5n(-3 + n)(n + -4) = 0

Reorder the terms:
5n(-3 + n)(-4 + n) = 0

Multiply (-3 + n) * (-4 + n)
5n(-3(-4 + n) + n(-4 + n)) = 0
5n((-4 * -3 + n * -3) + n(-4 + n)) = 0
5n((12 + -3n) + n(-4 + n)) = 0
5n(12 + -3n + (-4 * n + n * n)) = 0
5n(12 + -3n + (-4n + n2)) = 0

Combine like terms: -3n + -4n = -7n
5n(12 + -7n + n2) = 0
(12 * 5n + -7n * 5n + n2 * 5n) = 0
(60n + -35n2 + 5n3) = 0

Solving
60n + -35n2 + 5n3 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '5n'.
5n(12 + -7n + n2) = 0

Factor a trinomial.
5n((3 + -1n)(4 + -1n)) = 0

Ignore the factor 5.

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 '(3 + -1n)' equal to zero and attempt to solve:

Simplifying
3 + -1n = 0

Solving
3 + -1n = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1n = 0 + -3
-1n = 0 + -3

Combine like terms: 0 + -3 = -3
-1n = -3

Divide each side by '-1'.
n = 3

Simplifying
n = 3

Subproblem 3
Set the factor '(4 + -1n)' equal to zero and attempt to solve:

Simplifying
4 + -1n = 0

Solving
4 + -1n = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1n = 0 + -4
-1n = 0 + -4

Combine like terms: 0 + -4 = -4
-1n = -4

Divide each side by '-1'.
n = 4

Simplifying
n = 4
Solution
n = {0, 3, 4}

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