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Simplifying 14 + 3n = 8n + -1n(n + -4) Reorder the terms: 14 + 3n = 8n + -1n(-4 + n) 14 + 3n = 8n + (-4 * -1n + n * -1n) 14 + 3n = 8n + (4n + -1n2) Combine like terms: 8n + 4n = 12n 14 + 3n = 12n + -1n2 Solving 14 + 3n = 12n + -1n2 Solving for variable 'n'. Combine like terms: 3n + -12n = -9n 14 + -9n + n2 = 12n + -1n2 + -12n + n2 Reorder the terms: 14 + -9n + n2 = 12n + -12n + -1n2 + n2 Combine like terms: 12n + -12n = 0 14 + -9n + n2 = 0 + -1n2 + n2 14 + -9n + n2 = -1n2 + n2 Combine like terms: -1n2 + n2 = 0 14 + -9n + n2 = 0 Factor a trinomial. (2 + -1n)(7 + -1n) = 0Subproblem 1
Set the factor '(2 + -1n)' equal to zero and attempt to solve: Simplifying 2 + -1n = 0 Solving 2 + -1n = 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 + -1n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1n = 0 + -2 -1n = 0 + -2 Combine like terms: 0 + -2 = -2 -1n = -2 Divide each side by '-1'. n = 2 Simplifying n = 2Subproblem 2
Set the factor '(7 + -1n)' equal to zero and attempt to solve: Simplifying 7 + -1n = 0 Solving 7 + -1n = 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 + -1n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1n = 0 + -7 -1n = 0 + -7 Combine like terms: 0 + -7 = -7 -1n = -7 Divide each side by '-1'. n = 7 Simplifying n = 7Solution
n = {2, 7}
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