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Simplifying 0 = 2n(n + -1)(n + -3) Reorder the terms: 0 = 2n(-1 + n)(n + -3) Reorder the terms: 0 = 2n(-1 + n)(-3 + n) Multiply (-1 + n) * (-3 + n) 0 = 2n(-1(-3 + n) + n(-3 + n)) 0 = 2n((-3 * -1 + n * -1) + n(-3 + n)) 0 = 2n((3 + -1n) + n(-3 + n)) 0 = 2n(3 + -1n + (-3 * n + n * n)) 0 = 2n(3 + -1n + (-3n + n2)) Combine like terms: -1n + -3n = -4n 0 = 2n(3 + -4n + n2) 0 = (3 * 2n + -4n * 2n + n2 * 2n) 0 = (6n + -8n2 + 2n3) Solving 0 = 6n + -8n2 + 2n3 Solving for variable 'n'. Remove the zero: -6n + 8n2 + -2n3 = 6n + -8n2 + 2n3 + -6n + 8n2 + -2n3 Reorder the terms: -6n + 8n2 + -2n3 = 6n + -6n + -8n2 + 8n2 + 2n3 + -2n3 Combine like terms: 6n + -6n = 0 -6n + 8n2 + -2n3 = 0 + -8n2 + 8n2 + 2n3 + -2n3 -6n + 8n2 + -2n3 = -8n2 + 8n2 + 2n3 + -2n3 Combine like terms: -8n2 + 8n2 = 0 -6n + 8n2 + -2n3 = 0 + 2n3 + -2n3 -6n + 8n2 + -2n3 = 2n3 + -2n3 Combine like terms: 2n3 + -2n3 = 0 -6n + 8n2 + -2n3 = 0 Factor out the Greatest Common Factor (GCF), '2n'. 2n(-3 + 4n + -1n2) = 0 Factor a trinomial. 2n((-3 + n)(1 + -1n)) = 0 Ignore the factor 2.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 = 0Subproblem 2
Set the factor '(-3 + n)' equal to zero and attempt to solve: Simplifying -3 + n = 0 Solving -3 + n = 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 + n = 0 + 3 Combine like terms: -3 + 3 = 0 0 + n = 0 + 3 n = 0 + 3 Combine like terms: 0 + 3 = 3 n = 3 Simplifying n = 3Subproblem 3
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 = 1Solution
n = {0, 3, 1}
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