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Simplifying 5n2 + 175 = -60n Reorder the terms: 175 + 5n2 = -60n Solving 175 + 5n2 = -60n Solving for variable 'n'. Reorder the terms: 175 + 60n + 5n2 = -60n + 60n Combine like terms: -60n + 60n = 0 175 + 60n + 5n2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(35 + 12n + n2) = 0 Factor a trinomial. 5((7 + n)(5 + n)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(7 + n)' equal to zero and attempt to solve: Simplifying 7 + n = 0 Solving 7 + n = 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 + n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + n = 0 + -7 n = 0 + -7 Combine like terms: 0 + -7 = -7 n = -7 Simplifying n = -7Subproblem 2
Set the factor '(5 + n)' equal to zero and attempt to solve: Simplifying 5 + n = 0 Solving 5 + n = 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 + n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + n = 0 + -5 n = 0 + -5 Combine like terms: 0 + -5 = -5 n = -5 Simplifying n = -5Solution
n = {-7, -5}
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