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Simplifying 10n2 + 20n + -76 = 4 Reorder the terms: -76 + 20n + 10n2 = 4 Solving -76 + 20n + 10n2 = 4 Solving for variable 'n'. Reorder the terms: -76 + -4 + 20n + 10n2 = 4 + -4 Combine like terms: -76 + -4 = -80 -80 + 20n + 10n2 = 4 + -4 Combine like terms: 4 + -4 = 0 -80 + 20n + 10n2 = 0 Factor out the Greatest Common Factor (GCF), '10'. 10(-8 + 2n + n2) = 0 Factor a trinomial. 10((-4 + -1n)(2 + -1n)) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(-4 + -1n)' equal to zero and attempt to solve: Simplifying -4 + -1n = 0 Solving -4 + -1n = 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 + -1n = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1n = 0 + 4 -1n = 0 + 4 Combine like terms: 0 + 4 = 4 -1n = 4 Divide each side by '-1'. n = -4 Simplifying n = -4Subproblem 2
Set the factor '(2 + -1n)' equal to zero and attempt to solve: Simplifying 2 + -1n = 0 Solving 2 + -1n = 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 + -1n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1n = 0 + -2 -1n = 0 + -2 Combine like terms: 0 + -2 = -2 -1n = -2 Divide each side by '-1'. n = 2 Simplifying n = 2Solution
n = {-4, 2}
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