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Simplifying 12N2 + -102N + 126 = 0 Reorder the terms: 126 + -102N + 12N2 = 0 Solving 126 + -102N + 12N2 = 0 Solving for variable 'N'. Factor out the Greatest Common Factor (GCF), '6'. 6(21 + -17N + 2N2) = 0 Factor a trinomial. 6((3 + -2N)(7 + -1N)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(3 + -2N)' equal to zero and attempt to solve: Simplifying 3 + -2N = 0 Solving 3 + -2N = 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 + -2N = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2N = 0 + -3 -2N = 0 + -3 Combine like terms: 0 + -3 = -3 -2N = -3 Divide each side by '-2'. N = 1.5 Simplifying N = 1.5Subproblem 2
Set the factor '(7 + -1N)' equal to zero and attempt to solve: Simplifying 7 + -1N = 0 Solving 7 + -1N = 0 Move all terms containing N to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1N = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1N = 0 + -7 -1N = 0 + -7 Combine like terms: 0 + -7 = -7 -1N = -7 Divide each side by '-1'. N = 7 Simplifying N = 7Solution
N = {1.5, 7}
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