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Simplifying (3n + 8)(n + -1) = 0 Reorder the terms: (8 + 3n)(n + -1) = 0 Reorder the terms: (8 + 3n)(-1 + n) = 0 Multiply (8 + 3n) * (-1 + n) (8(-1 + n) + 3n * (-1 + n)) = 0 ((-1 * 8 + n * 8) + 3n * (-1 + n)) = 0 ((-8 + 8n) + 3n * (-1 + n)) = 0 (-8 + 8n + (-1 * 3n + n * 3n)) = 0 (-8 + 8n + (-3n + 3n2)) = 0 Combine like terms: 8n + -3n = 5n (-8 + 5n + 3n2) = 0 Solving -8 + 5n + 3n2 = 0 Solving for variable 'n'. Factor a trinomial. (-8 + -3n)(1 + -1n) = 0Subproblem 1
Set the factor '(-8 + -3n)' equal to zero and attempt to solve: Simplifying -8 + -3n = 0 Solving -8 + -3n = 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 + -3n = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -3n = 0 + 8 -3n = 0 + 8 Combine like terms: 0 + 8 = 8 -3n = 8 Divide each side by '-3'. n = -2.666666667 Simplifying n = -2.666666667Subproblem 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 = {-2.666666667, 1}
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