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Simplifying 8n3 + 8n2 + -126n = 0 Reorder the terms: -126n + 8n2 + 8n3 = 0 Solving -126n + 8n2 + 8n3 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2n'. 2n(-63 + 4n + 4n2) = 0 Factor a trinomial. 2n((-9 + -2n)(7 + -2n)) = 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 '(-9 + -2n)' equal to zero and attempt to solve: Simplifying -9 + -2n = 0 Solving -9 + -2n = 0 Move all terms containing n to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -2n = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -2n = 0 + 9 -2n = 0 + 9 Combine like terms: 0 + 9 = 9 -2n = 9 Divide each side by '-2'. n = -4.5 Simplifying n = -4.5Subproblem 3
Set the factor '(7 + -2n)' equal to zero and attempt to solve: Simplifying 7 + -2n = 0 Solving 7 + -2n = 0 Move all terms containing n to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -2n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2n = 0 + -7 -2n = 0 + -7 Combine like terms: 0 + -7 = -7 -2n = -7 Divide each side by '-2'. n = 3.5 Simplifying n = 3.5Solution
n = {0, -4.5, 3.5}
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