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Simplifying 4(4n + 5)(8n + 3) = 0 Reorder the terms: 4(5 + 4n)(8n + 3) = 0 Reorder the terms: 4(5 + 4n)(3 + 8n) = 0 Multiply (5 + 4n) * (3 + 8n) 4(5(3 + 8n) + 4n * (3 + 8n)) = 0 4((3 * 5 + 8n * 5) + 4n * (3 + 8n)) = 0 4((15 + 40n) + 4n * (3 + 8n)) = 0 4(15 + 40n + (3 * 4n + 8n * 4n)) = 0 4(15 + 40n + (12n + 32n2)) = 0 Combine like terms: 40n + 12n = 52n 4(15 + 52n + 32n2) = 0 (15 * 4 + 52n * 4 + 32n2 * 4) = 0 (60 + 208n + 128n2) = 0 Solving 60 + 208n + 128n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '4'. 4(15 + 52n + 32n2) = 0 Factor a trinomial. 4((5 + 4n)(3 + 8n)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(5 + 4n)' equal to zero and attempt to solve: Simplifying 5 + 4n = 0 Solving 5 + 4n = 0 Move all terms containing n to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 4n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 4n = 0 + -5 4n = 0 + -5 Combine like terms: 0 + -5 = -5 4n = -5 Divide each side by '4'. n = -1.25 Simplifying n = -1.25Subproblem 2
Set the factor '(3 + 8n)' equal to zero and attempt to solve: Simplifying 3 + 8n = 0 Solving 3 + 8n = 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 + 8n = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 8n = 0 + -3 8n = 0 + -3 Combine like terms: 0 + -3 = -3 8n = -3 Divide each side by '8'. n = -0.375 Simplifying n = -0.375Solution
n = {-1.25, -0.375}
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