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Simplifying 5n2 + 17n = 12 Reorder the terms: 17n + 5n2 = 12 Solving 17n + 5n2 = 12 Solving for variable 'n'. Reorder the terms: -12 + 17n + 5n2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + 17n + 5n2 = 0 Factor a trinomial. (-4 + -1n)(3 + -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 '(3 + -5n)' equal to zero and attempt to solve: Simplifying 3 + -5n = 0 Solving 3 + -5n = 0 Move all terms containing n to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -5n = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5n = 0 + -3 -5n = 0 + -3 Combine like terms: 0 + -3 = -3 -5n = -3 Divide each side by '-5'. n = 0.6 Simplifying n = 0.6Solution
n = {-4, 0.6}
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