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Simplifying 8n2 + 23n = 3 Reorder the terms: 23n + 8n2 = 3 Solving 23n + 8n2 = 3 Solving for variable 'n'. Reorder the terms: -3 + 23n + 8n2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + 23n + 8n2 = 0 Factor a trinomial. (-3 + -1n)(1 + -8n) = 0Subproblem 1
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 = -3Subproblem 2
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 = 0.125Solution
n = {-3, 0.125}
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