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Simplifying 15n2 + -27n + -6 = 7n2 + 5n + -30 Reorder the terms: -6 + -27n + 15n2 = 7n2 + 5n + -30 Reorder the terms: -6 + -27n + 15n2 = -30 + 5n + 7n2 Solving -6 + -27n + 15n2 = -30 + 5n + 7n2 Solving for variable 'n'. Reorder the terms: -6 + 30 + -27n + -5n + 15n2 + -7n2 = -30 + 5n + 7n2 + 30 + -5n + -7n2 Combine like terms: -6 + 30 = 24 24 + -27n + -5n + 15n2 + -7n2 = -30 + 5n + 7n2 + 30 + -5n + -7n2 Combine like terms: -27n + -5n = -32n 24 + -32n + 15n2 + -7n2 = -30 + 5n + 7n2 + 30 + -5n + -7n2 Combine like terms: 15n2 + -7n2 = 8n2 24 + -32n + 8n2 = -30 + 5n + 7n2 + 30 + -5n + -7n2 Reorder the terms: 24 + -32n + 8n2 = -30 + 30 + 5n + -5n + 7n2 + -7n2 Combine like terms: -30 + 30 = 0 24 + -32n + 8n2 = 0 + 5n + -5n + 7n2 + -7n2 24 + -32n + 8n2 = 5n + -5n + 7n2 + -7n2 Combine like terms: 5n + -5n = 0 24 + -32n + 8n2 = 0 + 7n2 + -7n2 24 + -32n + 8n2 = 7n2 + -7n2 Combine like terms: 7n2 + -7n2 = 0 24 + -32n + 8n2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(3 + -4n + n2) = 0 Factor a trinomial. 8((1 + -1n)(3 + -1n)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(1 + -1n)' equal to zero and attempt to solve: Simplifying 1 + -1n = 0 Solving 1 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1n = 0 + -1 -1n = 0 + -1 Combine like terms: 0 + -1 = -1 -1n = -1 Divide each side by '-1'. n = 1 Simplifying n = 1Subproblem 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 = {1, 3}
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