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Simplifying (4n + 5)(n + 4) = 0 Reorder the terms: (5 + 4n)(n + 4) = 0 Reorder the terms: (5 + 4n)(4 + n) = 0 Multiply (5 + 4n) * (4 + n) (5(4 + n) + 4n * (4 + n)) = 0 ((4 * 5 + n * 5) + 4n * (4 + n)) = 0 ((20 + 5n) + 4n * (4 + n)) = 0 (20 + 5n + (4 * 4n + n * 4n)) = 0 (20 + 5n + (16n + 4n2)) = 0 Combine like terms: 5n + 16n = 21n (20 + 21n + 4n2) = 0 Solving 20 + 21n + 4n2 = 0 Solving for variable 'n'. Factor a trinomial. (4 + n)(5 + 4n) = 0Subproblem 1
Set the factor '(4 + n)' equal to zero and attempt to solve: Simplifying 4 + n = 0 Solving 4 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + n = 0 + -4 n = 0 + -4 Combine like terms: 0 + -4 = -4 n = -4 Simplifying n = -4Subproblem 2
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 = -1.25Solution
n = {-4, -1.25}
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