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Simplifying 14n2 = 12n2 + -40n + -200 Reorder the terms: 14n2 = -200 + -40n + 12n2 Solving 14n2 = -200 + -40n + 12n2 Solving for variable 'n'. Reorder the terms: 200 + 40n + 14n2 + -12n2 = -200 + -40n + 12n2 + 200 + 40n + -12n2 Combine like terms: 14n2 + -12n2 = 2n2 200 + 40n + 2n2 = -200 + -40n + 12n2 + 200 + 40n + -12n2 Reorder the terms: 200 + 40n + 2n2 = -200 + 200 + -40n + 40n + 12n2 + -12n2 Combine like terms: -200 + 200 = 0 200 + 40n + 2n2 = 0 + -40n + 40n + 12n2 + -12n2 200 + 40n + 2n2 = -40n + 40n + 12n2 + -12n2 Combine like terms: -40n + 40n = 0 200 + 40n + 2n2 = 0 + 12n2 + -12n2 200 + 40n + 2n2 = 12n2 + -12n2 Combine like terms: 12n2 + -12n2 = 0 200 + 40n + 2n2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(100 + 20n + n2) = 0 Factor a trinomial. 2((10 + n)(10 + n)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(10 + n)' equal to zero and attempt to solve: Simplifying 10 + n = 0 Solving 10 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + n = 0 + -10 Combine like terms: 10 + -10 = 0 0 + n = 0 + -10 n = 0 + -10 Combine like terms: 0 + -10 = -10 n = -10 Simplifying n = -10Subproblem 2
Set the factor '(10 + n)' equal to zero and attempt to solve: Simplifying 10 + n = 0 Solving 10 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + n = 0 + -10 Combine like terms: 10 + -10 = 0 0 + n = 0 + -10 n = 0 + -10 Combine like terms: 0 + -10 = -10 n = -10 Simplifying n = -10Solution
n = {-10, -10}
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