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Simplifying (n + -8)(8n + -1) = 0 Reorder the terms: (-8 + n)(8n + -1) = 0 Reorder the terms: (-8 + n)(-1 + 8n) = 0 Multiply (-8 + n) * (-1 + 8n) (-8(-1 + 8n) + n(-1 + 8n)) = 0 ((-1 * -8 + 8n * -8) + n(-1 + 8n)) = 0 ((8 + -64n) + n(-1 + 8n)) = 0 (8 + -64n + (-1 * n + 8n * n)) = 0 (8 + -64n + (-1n + 8n2)) = 0 Combine like terms: -64n + -1n = -65n (8 + -65n + 8n2) = 0 Solving 8 + -65n + 8n2 = 0 Solving for variable 'n'. Factor a trinomial. (1 + -8n)(8 + -1n) = 0Subproblem 1
Set the factor '(1 + -8n)' equal to zero and attempt to solve: Simplifying 1 + -8n = 0 Solving 1 + -8n = 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 + -8n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -8n = 0 + -1 -8n = 0 + -1 Combine like terms: 0 + -1 = -1 -8n = -1 Divide each side by '-8'. n = 0.125 Simplifying n = 0.125Subproblem 2
Set the factor '(8 + -1n)' equal to zero and attempt to solve: Simplifying 8 + -1n = 0 Solving 8 + -1n = 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 + -1n = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1n = 0 + -8 -1n = 0 + -8 Combine like terms: 0 + -8 = -8 -1n = -8 Divide each side by '-1'. n = 8 Simplifying n = 8Solution
n = {0.125, 8}
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