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Simplifying (8n + -3)(n + -5) = 0 Reorder the terms: (-3 + 8n)(n + -5) = 0 Reorder the terms: (-3 + 8n)(-5 + n) = 0 Multiply (-3 + 8n) * (-5 + n) (-3(-5 + n) + 8n * (-5 + n)) = 0 ((-5 * -3 + n * -3) + 8n * (-5 + n)) = 0 ((15 + -3n) + 8n * (-5 + n)) = 0 (15 + -3n + (-5 * 8n + n * 8n)) = 0 (15 + -3n + (-40n + 8n2)) = 0 Combine like terms: -3n + -40n = -43n (15 + -43n + 8n2) = 0 Solving 15 + -43n + 8n2 = 0 Solving for variable 'n'. Factor a trinomial. (3 + -8n)(5 + -1n) = 0Subproblem 1
Set the factor '(3 + -8n)' equal to zero and attempt to solve: Simplifying 3 + -8n = 0 Solving 3 + -8n = 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 + -8n = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -8n = 0 + -3 -8n = 0 + -3 Combine like terms: 0 + -3 = -3 -8n = -3 Divide each side by '-8'. n = 0.375 Simplifying n = 0.375Subproblem 2
Set the factor '(5 + -1n)' equal to zero and attempt to solve: Simplifying 5 + -1n = 0 Solving 5 + -1n = 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 + -1n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1n = 0 + -5 -1n = 0 + -5 Combine like terms: 0 + -5 = -5 -1n = -5 Divide each side by '-1'. n = 5 Simplifying n = 5Solution
n = {0.375, 5}
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