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Simplifying (7n + 8)(8n + -3) = 0 Reorder the terms: (8 + 7n)(8n + -3) = 0 Reorder the terms: (8 + 7n)(-3 + 8n) = 0 Multiply (8 + 7n) * (-3 + 8n) (8(-3 + 8n) + 7n * (-3 + 8n)) = 0 ((-3 * 8 + 8n * 8) + 7n * (-3 + 8n)) = 0 ((-24 + 64n) + 7n * (-3 + 8n)) = 0 (-24 + 64n + (-3 * 7n + 8n * 7n)) = 0 (-24 + 64n + (-21n + 56n2)) = 0 Combine like terms: 64n + -21n = 43n (-24 + 43n + 56n2) = 0 Solving -24 + 43n + 56n2 = 0 Solving for variable 'n'. Factor a trinomial. (-8 + -7n)(3 + -8n) = 0Subproblem 1
Set the factor '(-8 + -7n)' equal to zero and attempt to solve: Simplifying -8 + -7n = 0 Solving -8 + -7n = 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 + -7n = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -7n = 0 + 8 -7n = 0 + 8 Combine like terms: 0 + 8 = 8 -7n = 8 Divide each side by '-7'. n = -1.142857143 Simplifying n = -1.142857143Subproblem 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 = {-1.142857143, 0.375}
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