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Simplifying n(n + -1)(n + -2) = 0 Reorder the terms: n(-1 + n)(n + -2) = 0 Reorder the terms: n(-1 + n)(-2 + n) = 0 Multiply (-1 + n) * (-2 + n) n(-1(-2 + n) + n(-2 + n)) = 0 n((-2 * -1 + n * -1) + n(-2 + n)) = 0 n((2 + -1n) + n(-2 + n)) = 0 n(2 + -1n + (-2 * n + n * n)) = 0 n(2 + -1n + (-2n + n2)) = 0 Combine like terms: -1n + -2n = -3n n(2 + -3n + n2) = 0 (2 * n + -3n * n + n2 * n) = 0 (2n + -3n2 + n3) = 0 Solving 2n + -3n2 + n3 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), 'n'. n(2 + -3n + n2) = 0 Factor a trinomial. n((1 + -1n)(2 + -1n)) = 0Subproblem 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 = 0Subproblem 2
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 = 1Subproblem 3
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 = 2Solution
n = {0, 1, 2}
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