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Simplifying (8n + -3)(7n + 5) = 0 Reorder the terms: (-3 + 8n)(7n + 5) = 0 Reorder the terms: (-3 + 8n)(5 + 7n) = 0 Multiply (-3 + 8n) * (5 + 7n) (-3(5 + 7n) + 8n * (5 + 7n)) = 0 ((5 * -3 + 7n * -3) + 8n * (5 + 7n)) = 0 ((-15 + -21n) + 8n * (5 + 7n)) = 0 (-15 + -21n + (5 * 8n + 7n * 8n)) = 0 (-15 + -21n + (40n + 56n2)) = 0 Combine like terms: -21n + 40n = 19n (-15 + 19n + 56n2) = 0 Solving -15 + 19n + 56n2 = 0 Solving for variable 'n'. Factor a trinomial. (-5 + -7n)(3 + -8n) = 0Subproblem 1
Set the factor '(-5 + -7n)' equal to zero and attempt to solve: Simplifying -5 + -7n = 0 Solving -5 + -7n = 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 + -7n = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -7n = 0 + 5 -7n = 0 + 5 Combine like terms: 0 + 5 = 5 -7n = 5 Divide each side by '-7'. n = -0.7142857143 Simplifying n = -0.7142857143Subproblem 2
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 = 0.375Solution
n = {-0.7142857143, 0.375}
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