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Simplifying 3n2 + 12n + 9 = 2n2 + 6n Reorder the terms: 9 + 12n + 3n2 = 2n2 + 6n Reorder the terms: 9 + 12n + 3n2 = 6n + 2n2 Solving 9 + 12n + 3n2 = 6n + 2n2 Solving for variable 'n'. Reorder the terms: 9 + 12n + -6n + 3n2 + -2n2 = 6n + 2n2 + -6n + -2n2 Combine like terms: 12n + -6n = 6n 9 + 6n + 3n2 + -2n2 = 6n + 2n2 + -6n + -2n2 Combine like terms: 3n2 + -2n2 = 1n2 9 + 6n + 1n2 = 6n + 2n2 + -6n + -2n2 Reorder the terms: 9 + 6n + 1n2 = 6n + -6n + 2n2 + -2n2 Combine like terms: 6n + -6n = 0 9 + 6n + 1n2 = 0 + 2n2 + -2n2 9 + 6n + 1n2 = 2n2 + -2n2 Combine like terms: 2n2 + -2n2 = 0 9 + 6n + 1n2 = 0 Factor a trinomial. (3 + n)(3 + n) = 0Subproblem 1
Set the factor '(3 + n)' equal to zero and attempt to solve: Simplifying 3 + n = 0 Solving 3 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + n = 0 + -3 Combine like terms: 3 + -3 = 0 0 + n = 0 + -3 n = 0 + -3 Combine like terms: 0 + -3 = -3 n = -3 Simplifying n = -3Subproblem 2
Set the factor '(3 + n)' equal to zero and attempt to solve: Simplifying 3 + n = 0 Solving 3 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + n = 0 + -3 Combine like terms: 3 + -3 = 0 0 + n = 0 + -3 n = 0 + -3 Combine like terms: 0 + -3 = -3 n = -3 Simplifying n = -3Solution
n = {-3, -3}
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