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Simplifying (8n + -5)(n + 2) = 0 Reorder the terms: (-5 + 8n)(n + 2) = 0 Reorder the terms: (-5 + 8n)(2 + n) = 0 Multiply (-5 + 8n) * (2 + n) (-5(2 + n) + 8n * (2 + n)) = 0 ((2 * -5 + n * -5) + 8n * (2 + n)) = 0 ((-10 + -5n) + 8n * (2 + n)) = 0 (-10 + -5n + (2 * 8n + n * 8n)) = 0 (-10 + -5n + (16n + 8n2)) = 0 Combine like terms: -5n + 16n = 11n (-10 + 11n + 8n2) = 0 Solving -10 + 11n + 8n2 = 0 Solving for variable 'n'. Factor a trinomial. (-2 + -1n)(5 + -8n) = 0Subproblem 1
Set the factor '(-2 + -1n)' equal to zero and attempt to solve: Simplifying -2 + -1n = 0 Solving -2 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1n = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1n = 0 + 2 -1n = 0 + 2 Combine like terms: 0 + 2 = 2 -1n = 2 Divide each side by '-1'. n = -2 Simplifying n = -2Subproblem 2
Set the factor '(5 + -8n)' equal to zero and attempt to solve: Simplifying 5 + -8n = 0 Solving 5 + -8n = 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 + -8n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -8n = 0 + -5 -8n = 0 + -5 Combine like terms: 0 + -5 = -5 -8n = -5 Divide each side by '-8'. n = 0.625 Simplifying n = 0.625Solution
n = {-2, 0.625}
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