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Simplifying 5n2 = -15n + 200 Reorder the terms: 5n2 = 200 + -15n Solving 5n2 = 200 + -15n Solving for variable 'n'. Reorder the terms: -200 + 15n + 5n2 = 200 + -15n + -200 + 15n Reorder the terms: -200 + 15n + 5n2 = 200 + -200 + -15n + 15n Combine like terms: 200 + -200 = 0 -200 + 15n + 5n2 = 0 + -15n + 15n -200 + 15n + 5n2 = -15n + 15n Combine like terms: -15n + 15n = 0 -200 + 15n + 5n2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-40 + 3n + n2) = 0 Factor a trinomial. 5((-8 + -1n)(5 + -1n)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-8 + -1n)' equal to zero and attempt to solve: Simplifying -8 + -1n = 0 Solving -8 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -1n = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1n = 0 + 8 -1n = 0 + 8 Combine like terms: 0 + 8 = 8 -1n = 8 Divide each side by '-1'. n = -8 Simplifying n = -8Subproblem 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 = {-8, 5}
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