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Simplifying 3n2 + -7n + 6 = 3n + -2 Reorder the terms: 6 + -7n + 3n2 = 3n + -2 Reorder the terms: 6 + -7n + 3n2 = -2 + 3n Solving 6 + -7n + 3n2 = -2 + 3n Solving for variable 'n'. Reorder the terms: 6 + 2 + -7n + -3n + 3n2 = -2 + 3n + 2 + -3n Combine like terms: 6 + 2 = 8 8 + -7n + -3n + 3n2 = -2 + 3n + 2 + -3n Combine like terms: -7n + -3n = -10n 8 + -10n + 3n2 = -2 + 3n + 2 + -3n Reorder the terms: 8 + -10n + 3n2 = -2 + 2 + 3n + -3n Combine like terms: -2 + 2 = 0 8 + -10n + 3n2 = 0 + 3n + -3n 8 + -10n + 3n2 = 3n + -3n Combine like terms: 3n + -3n = 0 8 + -10n + 3n2 = 0 Factor a trinomial. (4 + -3n)(2 + -1n) = 0Subproblem 1
Set the factor '(4 + -3n)' equal to zero and attempt to solve: Simplifying 4 + -3n = 0 Solving 4 + -3n = 0 Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3n = 0 + -4 -3n = 0 + -4 Combine like terms: 0 + -4 = -4 -3n = -4 Divide each side by '-3'. n = 1.333333333 Simplifying n = 1.333333333Subproblem 2
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 = 2Solution
n = {1.333333333, 2}
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