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Simplifying 10n2 + 7 = -14n + 3n2 Reorder the terms: 7 + 10n2 = -14n + 3n2 Solving 7 + 10n2 = -14n + 3n2 Solving for variable 'n'. Reorder the terms: 7 + 14n + 10n2 + -3n2 = -14n + 3n2 + 14n + -3n2 Combine like terms: 10n2 + -3n2 = 7n2 7 + 14n + 7n2 = -14n + 3n2 + 14n + -3n2 Reorder the terms: 7 + 14n + 7n2 = -14n + 14n + 3n2 + -3n2 Combine like terms: -14n + 14n = 0 7 + 14n + 7n2 = 0 + 3n2 + -3n2 7 + 14n + 7n2 = 3n2 + -3n2 Combine like terms: 3n2 + -3n2 = 0 7 + 14n + 7n2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(1 + 2n + n2) = 0 Factor a trinomial. 7((1 + n)(1 + n)) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(1 + n)' equal to zero and attempt to solve: Simplifying 1 + n = 0 Solving 1 + n = 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 + n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + n = 0 + -1 n = 0 + -1 Combine like terms: 0 + -1 = -1 n = -1 Simplifying n = -1Subproblem 2
Set the factor '(1 + n)' equal to zero and attempt to solve: Simplifying 1 + n = 0 Solving 1 + n = 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 + n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + n = 0 + -1 n = 0 + -1 Combine like terms: 0 + -1 = -1 n = -1 Simplifying n = -1Solution
n = {-1, -1}
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