(n-0)(n-1)(n-2)(n-3)(n-4)=0

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Solution for (n-0)(n-1)(n-2)(n-3)(n-4)=0 equation: 


Simplifying
(n + 0)(n + -1)(n + -2)(n + -3)(n + -4) = 0

Reorder the terms:
(0 + n)(n + -1)(n + -2)(n + -3)(n + -4) = 0
Remove the zero:
(n)(n + -1)(n + -2)(n + -3)(n + -4) = 0

Reorder the terms:
n(-1 + n)(n + -2)(n + -3)(n + -4) = 0

Reorder the terms:
n(-1 + n)(-2 + n)(n + -3)(n + -4) = 0

Reorder the terms:
n(-1 + n)(-2 + n)(-3 + n)(n + -4) = 0

Reorder the terms:
n(-1 + n)(-2 + n)(-3 + n)(-4 + n) = 0

Multiply (-1 + n) * (-2 + n)
n(-1(-2 + n) + n(-2 + n))(-3 + n)(-4 + n) = 0
n((-2 * -1 + n * -1) + n(-2 + n))(-3 + n)(-4 + n) = 0
n((2 + -1n) + n(-2 + n))(-3 + n)(-4 + n) = 0
n(2 + -1n + (-2 * n + n * n))(-3 + n)(-4 + n) = 0
n(2 + -1n + (-2n + n2))(-3 + n)(-4 + n) = 0

Combine like terms: -1n + -2n = -3n
n(2 + -3n + n2)(-3 + n)(-4 + n) = 0

Multiply (2 + -3n + n2) * (-3 + n)
n(2(-3 + n) + -3n * (-3 + n) + n2(-3 + n))(-4 + n) = 0
n((-3 * 2 + n * 2) + -3n * (-3 + n) + n2(-3 + n))(-4 + n) = 0
n((-6 + 2n) + -3n * (-3 + n) + n2(-3 + n))(-4 + n) = 0
n(-6 + 2n + (-3 * -3n + n * -3n) + n2(-3 + n))(-4 + n) = 0
n(-6 + 2n + (9n + -3n2) + n2(-3 + n))(-4 + n) = 0
n(-6 + 2n + 9n + -3n2 + (-3 * n2 + n * n2))(-4 + n) = 0
n(-6 + 2n + 9n + -3n2 + (-3n2 + n3))(-4 + n) = 0

Combine like terms: 2n + 9n = 11n
n(-6 + 11n + -3n2 + -3n2 + n3)(-4 + n) = 0

Combine like terms: -3n2 + -3n2 = -6n2
n(-6 + 11n + -6n2 + n3)(-4 + n) = 0

Multiply (-6 + 11n + -6n2 + n3) * (-4 + n)
n(-6(-4 + n) + 11n * (-4 + n) + -6n2 * (-4 + n) + n3(-4 + n)) = 0
n((-4 * -6 + n * -6) + 11n * (-4 + n) + -6n2 * (-4 + n) + n3(-4 + n)) = 0
n((24 + -6n) + 11n * (-4 + n) + -6n2 * (-4 + n) + n3(-4 + n)) = 0
n(24 + -6n + (-4 * 11n + n * 11n) + -6n2 * (-4 + n) + n3(-4 + n)) = 0
n(24 + -6n + (-44n + 11n2) + -6n2 * (-4 + n) + n3(-4 + n)) = 0
n(24 + -6n + -44n + 11n2 + (-4 * -6n2 + n * -6n2) + n3(-4 + n)) = 0
n(24 + -6n + -44n + 11n2 + (24n2 + -6n3) + n3(-4 + n)) = 0
n(24 + -6n + -44n + 11n2 + 24n2 + -6n3 + (-4 * n3 + n * n3)) = 0
n(24 + -6n + -44n + 11n2 + 24n2 + -6n3 + (-4n3 + n4)) = 0

Combine like terms: -6n + -44n = -50n
n(24 + -50n + 11n2 + 24n2 + -6n3 + -4n3 + n4) = 0

Combine like terms: 11n2 + 24n2 = 35n2
n(24 + -50n + 35n2 + -6n3 + -4n3 + n4) = 0

Combine like terms: -6n3 + -4n3 = -10n3
n(24 + -50n + 35n2 + -10n3 + n4) = 0
(24 * n + -50n * n + 35n2 * n + -10n3 * n + n4 * n) = 0
(24n + -50n2 + 35n3 + -10n4 + n5) = 0

Solving
24n + -50n2 + 35n3 + -10n4 + n5 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), 'n'.
n(24 + -50n + 35n2 + -10n3 + n4) = 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 '(24 + -50n + 35n2 + -10n3 + n4)' equal to zero and attempt to solve:

Simplifying
24 + -50n + 35n2 + -10n3 + n4 = 0

Solving
24 + -50n + 35n2 + -10n3 + n4 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
n = {0}

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