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Simplifying 3n2 + 6n + -27 = 2n2 Reorder the terms: -27 + 6n + 3n2 = 2n2 Solving -27 + 6n + 3n2 = 2n2 Solving for variable 'n'. Combine like terms: 3n2 + -2n2 = 1n2 -27 + 6n + 1n2 = 2n2 + -2n2 Combine like terms: 2n2 + -2n2 = 0 -27 + 6n + 1n2 = 0 Factor a trinomial. (-9 + -1n)(3 + -1n) = 0Subproblem 1
Set the factor '(-9 + -1n)' equal to zero and attempt to solve: Simplifying -9 + -1n = 0 Solving -9 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1n = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1n = 0 + 9 -1n = 0 + 9 Combine like terms: 0 + 9 = 9 -1n = 9 Divide each side by '-1'. n = -9 Simplifying n = -9Subproblem 2
Set the factor '(3 + -1n)' equal to zero and attempt to solve: Simplifying 3 + -1n = 0 Solving 3 + -1n = 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 + -1n = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1n = 0 + -3 -1n = 0 + -3 Combine like terms: 0 + -3 = -3 -1n = -3 Divide each side by '-1'. n = 3 Simplifying n = 3Solution
n = {-9, 3}
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