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Simplifying (4n + 4)(5n + 8) = 0 Reorder the terms: (4 + 4n)(5n + 8) = 0 Reorder the terms: (4 + 4n)(8 + 5n) = 0 Multiply (4 + 4n) * (8 + 5n) (4(8 + 5n) + 4n * (8 + 5n)) = 0 ((8 * 4 + 5n * 4) + 4n * (8 + 5n)) = 0 ((32 + 20n) + 4n * (8 + 5n)) = 0 (32 + 20n + (8 * 4n + 5n * 4n)) = 0 (32 + 20n + (32n + 20n2)) = 0 Combine like terms: 20n + 32n = 52n (32 + 52n + 20n2) = 0 Solving 32 + 52n + 20n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '4'. 4(8 + 13n + 5n2) = 0 Factor a trinomial. 4((8 + 5n)(1 + n)) = 0 Ignore the factor 4.Subproblem 1
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 = -1.6Subproblem 2
Set the factor '(1 + n)' equal to zero and attempt to solve: Simplifying 1 + n = 0 Solving 1 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + n = 0 + -1 n = 0 + -1 Combine like terms: 0 + -1 = -1 n = -1 Simplifying n = -1Solution
n = {-1.6, -1}
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