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Simplifying (8n + -8)(5n + 7) = 0 Reorder the terms: (-8 + 8n)(5n + 7) = 0 Reorder the terms: (-8 + 8n)(7 + 5n) = 0 Multiply (-8 + 8n) * (7 + 5n) (-8(7 + 5n) + 8n * (7 + 5n)) = 0 ((7 * -8 + 5n * -8) + 8n * (7 + 5n)) = 0 ((-56 + -40n) + 8n * (7 + 5n)) = 0 (-56 + -40n + (7 * 8n + 5n * 8n)) = 0 (-56 + -40n + (56n + 40n2)) = 0 Combine like terms: -40n + 56n = 16n (-56 + 16n + 40n2) = 0 Solving -56 + 16n + 40n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '8'. 8(-7 + 2n + 5n2) = 0 Factor a trinomial. 8((-7 + -5n)(1 + -1n)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-7 + -5n)' equal to zero and attempt to solve: Simplifying -7 + -5n = 0 Solving -7 + -5n = 0 Move all terms containing n to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -5n = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -5n = 0 + 7 -5n = 0 + 7 Combine like terms: 0 + 7 = 7 -5n = 7 Divide each side by '-5'. n = -1.4 Simplifying n = -1.4Subproblem 2
Set the factor '(1 + -1n)' equal to zero and attempt to solve: Simplifying 1 + -1n = 0 Solving 1 + -1n = 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 + -1n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1n = 0 + -1 -1n = 0 + -1 Combine like terms: 0 + -1 = -1 -1n = -1 Divide each side by '-1'. n = 1 Simplifying n = 1Solution
n = {-1.4, 1}
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