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Simplifying 14n2 + -8n = 9n2 + 105 + -4n Reorder the terms: -8n + 14n2 = 9n2 + 105 + -4n Reorder the terms: -8n + 14n2 = 105 + -4n + 9n2 Solving -8n + 14n2 = 105 + -4n + 9n2 Solving for variable 'n'. Reorder the terms: -105 + -8n + 4n + 14n2 + -9n2 = 105 + -4n + 9n2 + -105 + 4n + -9n2 Combine like terms: -8n + 4n = -4n -105 + -4n + 14n2 + -9n2 = 105 + -4n + 9n2 + -105 + 4n + -9n2 Combine like terms: 14n2 + -9n2 = 5n2 -105 + -4n + 5n2 = 105 + -4n + 9n2 + -105 + 4n + -9n2 Reorder the terms: -105 + -4n + 5n2 = 105 + -105 + -4n + 4n + 9n2 + -9n2 Combine like terms: 105 + -105 = 0 -105 + -4n + 5n2 = 0 + -4n + 4n + 9n2 + -9n2 -105 + -4n + 5n2 = -4n + 4n + 9n2 + -9n2 Combine like terms: -4n + 4n = 0 -105 + -4n + 5n2 = 0 + 9n2 + -9n2 -105 + -4n + 5n2 = 9n2 + -9n2 Combine like terms: 9n2 + -9n2 = 0 -105 + -4n + 5n2 = 0 Factor a trinomial. (-21 + -5n)(5 + -1n) = 0Subproblem 1
Set the factor '(-21 + -5n)' equal to zero and attempt to solve: Simplifying -21 + -5n = 0 Solving -21 + -5n = 0 Move all terms containing n to the left, all other terms to the right. Add '21' to each side of the equation. -21 + 21 + -5n = 0 + 21 Combine like terms: -21 + 21 = 0 0 + -5n = 0 + 21 -5n = 0 + 21 Combine like terms: 0 + 21 = 21 -5n = 21 Divide each side by '-5'. n = -4.2 Simplifying n = -4.2Subproblem 2
Set the factor '(5 + -1n)' equal to zero and attempt to solve: Simplifying 5 + -1n = 0 Solving 5 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1n = 0 + -5 -1n = 0 + -5 Combine like terms: 0 + -5 = -5 -1n = -5 Divide each side by '-1'. n = 5 Simplifying n = 5Solution
n = {-4.2, 5}
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