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Simplifying 3n2 + -23 = 13n + 7 Reorder the terms: -23 + 3n2 = 13n + 7 Reorder the terms: -23 + 3n2 = 7 + 13n Solving -23 + 3n2 = 7 + 13n Solving for variable 'n'. Reorder the terms: -23 + -7 + -13n + 3n2 = 7 + 13n + -7 + -13n Combine like terms: -23 + -7 = -30 -30 + -13n + 3n2 = 7 + 13n + -7 + -13n Reorder the terms: -30 + -13n + 3n2 = 7 + -7 + 13n + -13n Combine like terms: 7 + -7 = 0 -30 + -13n + 3n2 = 0 + 13n + -13n -30 + -13n + 3n2 = 13n + -13n Combine like terms: 13n + -13n = 0 -30 + -13n + 3n2 = 0 Factor a trinomial. (-5 + -3n)(6 + -1n) = 0Subproblem 1
Set the factor '(-5 + -3n)' equal to zero and attempt to solve: Simplifying -5 + -3n = 0 Solving -5 + -3n = 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 + -3n = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -3n = 0 + 5 -3n = 0 + 5 Combine like terms: 0 + 5 = 5 -3n = 5 Divide each side by '-3'. n = -1.666666667 Simplifying n = -1.666666667Subproblem 2
Set the factor '(6 + -1n)' equal to zero and attempt to solve: Simplifying 6 + -1n = 0 Solving 6 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1n = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1n = 0 + -6 -1n = 0 + -6 Combine like terms: 0 + -6 = -6 -1n = -6 Divide each side by '-1'. n = 6 Simplifying n = 6Solution
n = {-1.666666667, 6}
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