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Simplifying 5n2 = 8 + -18n Solving 5n2 = 8 + -18n Solving for variable 'n'. Reorder the terms: -8 + 18n + 5n2 = 8 + -18n + -8 + 18n Reorder the terms: -8 + 18n + 5n2 = 8 + -8 + -18n + 18n Combine like terms: 8 + -8 = 0 -8 + 18n + 5n2 = 0 + -18n + 18n -8 + 18n + 5n2 = -18n + 18n Combine like terms: -18n + 18n = 0 -8 + 18n + 5n2 = 0 Factor a trinomial. (-4 + -1n)(2 + -5n) = 0Subproblem 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 '(2 + -5n)' equal to zero and attempt to solve: Simplifying 2 + -5n = 0 Solving 2 + -5n = 0 Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -5n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5n = 0 + -2 -5n = 0 + -2 Combine like terms: 0 + -2 = -2 -5n = -2 Divide each side by '-5'. n = 0.4 Simplifying n = 0.4Solution
n = {-4, 0.4}
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