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Simplifying 3n2 + 14 = 8n2 + 3n Reorder the terms: 14 + 3n2 = 8n2 + 3n Reorder the terms: 14 + 3n2 = 3n + 8n2 Solving 14 + 3n2 = 3n + 8n2 Solving for variable 'n'. Reorder the terms: 14 + -3n + 3n2 + -8n2 = 3n + 8n2 + -3n + -8n2 Combine like terms: 3n2 + -8n2 = -5n2 14 + -3n + -5n2 = 3n + 8n2 + -3n + -8n2 Reorder the terms: 14 + -3n + -5n2 = 3n + -3n + 8n2 + -8n2 Combine like terms: 3n + -3n = 0 14 + -3n + -5n2 = 0 + 8n2 + -8n2 14 + -3n + -5n2 = 8n2 + -8n2 Combine like terms: 8n2 + -8n2 = 0 14 + -3n + -5n2 = 0 Factor a trinomial. (7 + -5n)(2 + n) = 0Subproblem 1
Set the factor '(7 + -5n)' equal to zero and attempt to solve: Simplifying 7 + -5n = 0 Solving 7 + -5n = 0 Move all terms containing n to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -5n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -5n = 0 + -7 -5n = 0 + -7 Combine like terms: 0 + -7 = -7 -5n = -7 Divide each side by '-5'. n = 1.4 Simplifying n = 1.4Subproblem 2
Set the factor '(2 + n)' equal to zero and attempt to solve: Simplifying 2 + n = 0 Solving 2 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + n = 0 + -2 n = 0 + -2 Combine like terms: 0 + -2 = -2 n = -2 Simplifying n = -2Solution
n = {1.4, -2}
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