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Simplifying 3n2 = 7n + 110 Reorder the terms: 3n2 = 110 + 7n Solving 3n2 = 110 + 7n Solving for variable 'n'. Reorder the terms: -110 + -7n + 3n2 = 110 + 7n + -110 + -7n Reorder the terms: -110 + -7n + 3n2 = 110 + -110 + 7n + -7n Combine like terms: 110 + -110 = 0 -110 + -7n + 3n2 = 0 + 7n + -7n -110 + -7n + 3n2 = 7n + -7n Combine like terms: 7n + -7n = 0 -110 + -7n + 3n2 = 0 Factor a trinomial. (-5 + -1n)(22 + -3n) = 0Subproblem 1
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 = -5Subproblem 2
Set the factor '(22 + -3n)' equal to zero and attempt to solve: Simplifying 22 + -3n = 0 Solving 22 + -3n = 0 Move all terms containing n to the left, all other terms to the right. Add '-22' to each side of the equation. 22 + -22 + -3n = 0 + -22 Combine like terms: 22 + -22 = 0 0 + -3n = 0 + -22 -3n = 0 + -22 Combine like terms: 0 + -22 = -22 -3n = -22 Divide each side by '-3'. n = 7.333333333 Simplifying n = 7.333333333Solution
n = {-5, 7.333333333}
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