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Simplifying 17n2 + -10n + -12 = 3n2 + -8 Reorder the terms: -12 + -10n + 17n2 = 3n2 + -8 Reorder the terms: -12 + -10n + 17n2 = -8 + 3n2 Solving -12 + -10n + 17n2 = -8 + 3n2 Solving for variable 'n'. Reorder the terms: -12 + 8 + -10n + 17n2 + -3n2 = -8 + 3n2 + 8 + -3n2 Combine like terms: -12 + 8 = -4 -4 + -10n + 17n2 + -3n2 = -8 + 3n2 + 8 + -3n2 Combine like terms: 17n2 + -3n2 = 14n2 -4 + -10n + 14n2 = -8 + 3n2 + 8 + -3n2 Reorder the terms: -4 + -10n + 14n2 = -8 + 8 + 3n2 + -3n2 Combine like terms: -8 + 8 = 0 -4 + -10n + 14n2 = 0 + 3n2 + -3n2 -4 + -10n + 14n2 = 3n2 + -3n2 Combine like terms: 3n2 + -3n2 = 0 -4 + -10n + 14n2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + -5n + 7n2) = 0 Factor a trinomial. 2((-2 + -7n)(1 + -1n)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + -7n)' equal to zero and attempt to solve: Simplifying -2 + -7n = 0 Solving -2 + -7n = 0 Move all terms containing n to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -7n = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -7n = 0 + 2 -7n = 0 + 2 Combine like terms: 0 + 2 = 2 -7n = 2 Divide each side by '-7'. n = -0.2857142857 Simplifying n = -0.2857142857Subproblem 2
Set the factor '(1 + -1n)' equal to zero and attempt to solve: Simplifying 1 + -1n = 0 Solving 1 + -1n = 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 + -1n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1n = 0 + -1 -1n = 0 + -1 Combine like terms: 0 + -1 = -1 -1n = -1 Divide each side by '-1'. n = 1 Simplifying n = 1Solution
n = {-0.2857142857, 1}
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