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Simplifying 14n2 + 116n + 126 = 0 Reorder the terms: 126 + 116n + 14n2 = 0 Solving 126 + 116n + 14n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2'. 2(63 + 58n + 7n2) = 0 Factor a trinomial. 2((7 + n)(9 + 7n)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + n)' equal to zero and attempt to solve: Simplifying 7 + n = 0 Solving 7 + n = 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 + n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + n = 0 + -7 n = 0 + -7 Combine like terms: 0 + -7 = -7 n = -7 Simplifying n = -7Subproblem 2
Set the factor '(9 + 7n)' equal to zero and attempt to solve: Simplifying 9 + 7n = 0 Solving 9 + 7n = 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 + 7n = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 7n = 0 + -9 7n = 0 + -9 Combine like terms: 0 + -9 = -9 7n = -9 Divide each side by '7'. n = -1.285714286 Simplifying n = -1.285714286Solution
n = {-7, -1.285714286}
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