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Simplifying 14 + 3n = 8n + -3n(n + -4) Reorder the terms: 14 + 3n = 8n + -3n(-4 + n) 14 + 3n = 8n + (-4 * -3n + n * -3n) 14 + 3n = 8n + (12n + -3n2) Combine like terms: 8n + 12n = 20n 14 + 3n = 20n + -3n2 Solving 14 + 3n = 20n + -3n2 Solving for variable 'n'. Combine like terms: 3n + -20n = -17n 14 + -17n + 3n2 = 20n + -3n2 + -20n + 3n2 Reorder the terms: 14 + -17n + 3n2 = 20n + -20n + -3n2 + 3n2 Combine like terms: 20n + -20n = 0 14 + -17n + 3n2 = 0 + -3n2 + 3n2 14 + -17n + 3n2 = -3n2 + 3n2 Combine like terms: -3n2 + 3n2 = 0 14 + -17n + 3n2 = 0 Factor a trinomial. (1 + -1n)(14 + -3n) = 0Subproblem 1
Set the factor '(1 + -1n)' equal to zero and attempt to solve: Simplifying 1 + -1n = 0 Solving 1 + -1n = 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 + -1n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1n = 0 + -1 -1n = 0 + -1 Combine like terms: 0 + -1 = -1 -1n = -1 Divide each side by '-1'. n = 1 Simplifying n = 1Subproblem 2
Set the factor '(14 + -3n)' equal to zero and attempt to solve: Simplifying 14 + -3n = 0 Solving 14 + -3n = 0 Move all terms containing n to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + -3n = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -3n = 0 + -14 -3n = 0 + -14 Combine like terms: 0 + -14 = -14 -3n = -14 Divide each side by '-3'. n = 4.666666667 Simplifying n = 4.666666667Solution
n = {1, 4.666666667}
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