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Simplifying n(n + 8)(n + -2) = 0 Reorder the terms: n(8 + n)(n + -2) = 0 Reorder the terms: n(8 + n)(-2 + n) = 0 Multiply (8 + n) * (-2 + n) n(8(-2 + n) + n(-2 + n)) = 0 n((-2 * 8 + n * 8) + n(-2 + n)) = 0 n((-16 + 8n) + n(-2 + n)) = 0 n(-16 + 8n + (-2 * n + n * n)) = 0 n(-16 + 8n + (-2n + n2)) = 0 Combine like terms: 8n + -2n = 6n n(-16 + 6n + n2) = 0 (-16 * n + 6n * n + n2 * n) = 0 (-16n + 6n2 + n3) = 0 Solving -16n + 6n2 + n3 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), 'n'. n(-16 + 6n + n2) = 0 Factor a trinomial. n((-8 + -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 '(-8 + -1n)' equal to zero and attempt to solve: Simplifying -8 + -1n = 0 Solving -8 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -1n = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1n = 0 + 8 -1n = 0 + 8 Combine like terms: 0 + 8 = 8 -1n = 8 Divide each side by '-1'. n = -8 Simplifying n = -8Subproblem 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, -8, 2}
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