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Simplifying 7n2 + -7n = 140 Reorder the terms: -7n + 7n2 = 140 Solving -7n + 7n2 = 140 Solving for variable 'n'. Reorder the terms: -140 + -7n + 7n2 = 140 + -140 Combine like terms: 140 + -140 = 0 -140 + -7n + 7n2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(-20 + -1n + n2) = 0 Factor a trinomial. 7((-4 + -1n)(5 + -1n)) = 0 Ignore the factor 7.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 '(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 = {-4, 5}
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