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Simplifying 21n2 + 138n = -72 Reorder the terms: 138n + 21n2 = -72 Solving 138n + 21n2 = -72 Solving for variable 'n'. Reorder the terms: 72 + 138n + 21n2 = -72 + 72 Combine like terms: -72 + 72 = 0 72 + 138n + 21n2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(24 + 46n + 7n2) = 0 Factor a trinomial. 3((6 + n)(4 + 7n)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(6 + n)' equal to zero and attempt to solve: Simplifying 6 + n = 0 Solving 6 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + n = 0 + -6 Combine like terms: 6 + -6 = 0 0 + n = 0 + -6 n = 0 + -6 Combine like terms: 0 + -6 = -6 n = -6 Simplifying n = -6Subproblem 2
Set the factor '(4 + 7n)' equal to zero and attempt to solve: Simplifying 4 + 7n = 0 Solving 4 + 7n = 0 Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 7n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 7n = 0 + -4 7n = 0 + -4 Combine like terms: 0 + -4 = -4 7n = -4 Divide each side by '7'. n = -0.5714285714 Simplifying n = -0.5714285714Solution
n = {-6, -0.5714285714}
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