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Simplifying 16n2 + -21n = 8n2 + 9 Reorder the terms: -21n + 16n2 = 8n2 + 9 Reorder the terms: -21n + 16n2 = 9 + 8n2 Solving -21n + 16n2 = 9 + 8n2 Solving for variable 'n'. Reorder the terms: -9 + -21n + 16n2 + -8n2 = 9 + 8n2 + -9 + -8n2 Combine like terms: 16n2 + -8n2 = 8n2 -9 + -21n + 8n2 = 9 + 8n2 + -9 + -8n2 Reorder the terms: -9 + -21n + 8n2 = 9 + -9 + 8n2 + -8n2 Combine like terms: 9 + -9 = 0 -9 + -21n + 8n2 = 0 + 8n2 + -8n2 -9 + -21n + 8n2 = 8n2 + -8n2 Combine like terms: 8n2 + -8n2 = 0 -9 + -21n + 8n2 = 0 Factor a trinomial. (-3 + -8n)(3 + -1n) = 0Subproblem 1
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 = -0.375Subproblem 2
Set the factor '(3 + -1n)' equal to zero and attempt to solve: Simplifying 3 + -1n = 0 Solving 3 + -1n = 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 + -1n = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1n = 0 + -3 -1n = 0 + -3 Combine like terms: 0 + -3 = -3 -1n = -3 Divide each side by '-1'. n = 3 Simplifying n = 3Solution
n = {-0.375, 3}
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