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Simplifying 40n2 + 384n + 512 = 0 Reorder the terms: 512 + 384n + 40n2 = 0 Solving 512 + 384n + 40n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '8'. 8(64 + 48n + 5n2) = 0 Factor a trinomial. 8((8 + n)(8 + 5n)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(8 + n)' equal to zero and attempt to solve: Simplifying 8 + n = 0 Solving 8 + n = 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 + n = 0 + -8 Combine like terms: 8 + -8 = 0 0 + n = 0 + -8 n = 0 + -8 Combine like terms: 0 + -8 = -8 n = -8 Simplifying n = -8Subproblem 2
Set the factor '(8 + 5n)' equal to zero and attempt to solve: Simplifying 8 + 5n = 0 Solving 8 + 5n = 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 + 5n = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 5n = 0 + -8 5n = 0 + -8 Combine like terms: 0 + -8 = -8 5n = -8 Divide each side by '5'. n = -1.6 Simplifying n = -1.6Solution
n = {-8, -1.6}
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