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Simplifying 5n2 = 40n + -35 Reorder the terms: 5n2 = -35 + 40n Solving 5n2 = -35 + 40n Solving for variable 'n'. Reorder the terms: 35 + -40n + 5n2 = -35 + 40n + 35 + -40n Reorder the terms: 35 + -40n + 5n2 = -35 + 35 + 40n + -40n Combine like terms: -35 + 35 = 0 35 + -40n + 5n2 = 0 + 40n + -40n 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((1 + -1n)(7 + -1n)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(1 + -1n)' equal to zero and attempt to solve: Simplifying 1 + -1n = 0 Solving 1 + -1n = 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 + -1n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1n = 0 + -1 -1n = 0 + -1 Combine like terms: 0 + -1 = -1 -1n = -1 Divide each side by '-1'. n = 1 Simplifying n = 1Subproblem 2
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 = 7Solution
n = {1, 7}
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