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Simplifying 5n2 + 35 = -40n Reorder the terms: 35 + 5n2 = -40n Solving 35 + 5n2 = -40n Solving for variable 'n'. Reorder the terms: 35 + 40n + 5n2 = -40n + 40n Combine like terms: -40n + 40n = 0 35 + 40n + 5n2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(7 + 8n + n2) = 0 Factor a trinomial. 5((7 + n)(1 + 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 '(1 + n)' equal to zero and attempt to solve: Simplifying 1 + n = 0 Solving 1 + n = 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 + n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + n = 0 + -1 n = 0 + -1 Combine like terms: 0 + -1 = -1 n = -1 Simplifying n = -1Solution
n = {-7, -1}
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