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Simplifying 2n2 + 4n + -74 = -4 Reorder the terms: -74 + 4n + 2n2 = -4 Solving -74 + 4n + 2n2 = -4 Solving for variable 'n'. Reorder the terms: -74 + 4 + 4n + 2n2 = -4 + 4 Combine like terms: -74 + 4 = -70 -70 + 4n + 2n2 = -4 + 4 Combine like terms: -4 + 4 = 0 -70 + 4n + 2n2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-35 + 2n + n2) = 0 Factor a trinomial. 2((-7 + -1n)(5 + -1n)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7 + -1n)' equal to zero and attempt to solve: Simplifying -7 + -1n = 0 Solving -7 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -1n = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1n = 0 + 7 -1n = 0 + 7 Combine like terms: 0 + 7 = 7 -1n = 7 Divide each side by '-1'. n = -7 Simplifying n = -7Subproblem 2
Set the factor '(5 + -1n)' equal to zero and attempt to solve: Simplifying 5 + -1n = 0 Solving 5 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1n = 0 + -5 -1n = 0 + -5 Combine like terms: 0 + -5 = -5 -1n = -5 Divide each side by '-1'. n = 5 Simplifying n = 5Solution
n = {-7, 5}
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