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Simplifying (5n + -3)(8 + n) = 0 Reorder the terms: (-3 + 5n)(8 + n) = 0 Multiply (-3 + 5n) * (8 + n) (-3(8 + n) + 5n * (8 + n)) = 0 ((8 * -3 + n * -3) + 5n * (8 + n)) = 0 ((-24 + -3n) + 5n * (8 + n)) = 0 (-24 + -3n + (8 * 5n + n * 5n)) = 0 (-24 + -3n + (40n + 5n2)) = 0 Combine like terms: -3n + 40n = 37n (-24 + 37n + 5n2) = 0 Solving -24 + 37n + 5n2 = 0 Solving for variable 'n'. Factor a trinomial. (-8 + -1n)(3 + -5n) = 0Subproblem 1
Set the factor '(-8 + -1n)' equal to zero and attempt to solve: Simplifying -8 + -1n = 0 Solving -8 + -1n = 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 + -1n = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1n = 0 + 8 -1n = 0 + 8 Combine like terms: 0 + 8 = 8 -1n = 8 Divide each side by '-1'. n = -8 Simplifying n = -8Subproblem 2
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 = 0.6Solution
n = {-8, 0.6}
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