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

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


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

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

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

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

Combine like terms: -2n + -3n = -5n
n(6 + -5n + n2) = 0
(6 * n + -5n * n + n2 * n) = 0
(6n + -5n2 + n3) = 0

Solving
6n + -5n2 + n3 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), 'n'.
n(6 + -5n + n2) = 0

Factor a trinomial.
n((2 + -1n)(3 + -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 '(2 + -1n)' equal to zero and attempt to solve: Simplifying 2 + -1n = 0 Solving 2 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1n = 0 + -2 -1n = 0 + -2 Combine like terms: 0 + -2 = -2 -1n = -2 Divide each side by '-1'. n = 2 Simplifying n = 2

Subproblem 3

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

Solution

n = {0, 2, 3}

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