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Simplifying 72n2 + -66n + -72 = -8n2 + 6n Reorder the terms: -72 + -66n + 72n2 = -8n2 + 6n Reorder the terms: -72 + -66n + 72n2 = 6n + -8n2 Solving -72 + -66n + 72n2 = 6n + -8n2 Solving for variable 'n'. Reorder the terms: -72 + -66n + -6n + 72n2 + 8n2 = 6n + -8n2 + -6n + 8n2 Combine like terms: -66n + -6n = -72n -72 + -72n + 72n2 + 8n2 = 6n + -8n2 + -6n + 8n2 Combine like terms: 72n2 + 8n2 = 80n2 -72 + -72n + 80n2 = 6n + -8n2 + -6n + 8n2 Reorder the terms: -72 + -72n + 80n2 = 6n + -6n + -8n2 + 8n2 Combine like terms: 6n + -6n = 0 -72 + -72n + 80n2 = 0 + -8n2 + 8n2 -72 + -72n + 80n2 = -8n2 + 8n2 Combine like terms: -8n2 + 8n2 = 0 -72 + -72n + 80n2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-9 + -9n + 10n2) = 0 Factor a trinomial. 8((-3 + -5n)(3 + -2n)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-3 + -5n)' equal to zero and attempt to solve: Simplifying -3 + -5n = 0 Solving -3 + -5n = 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 + -5n = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -5n = 0 + 3 -5n = 0 + 3 Combine like terms: 0 + 3 = 3 -5n = 3 Divide each side by '-5'. n = -0.6 Simplifying n = -0.6Subproblem 2
Set the factor '(3 + -2n)' equal to zero and attempt to solve: Simplifying 3 + -2n = 0 Solving 3 + -2n = 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 + -2n = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2n = 0 + -3 -2n = 0 + -3 Combine like terms: 0 + -3 = -3 -2n = -3 Divide each side by '-2'. n = 1.5 Simplifying n = 1.5Solution
n = {-0.6, 1.5}
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