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Simplifying 3n2 = -5n + 8 Reorder the terms: 3n2 = 8 + -5n Solving 3n2 = 8 + -5n Solving for variable 'n'. Reorder the terms: -8 + 5n + 3n2 = 8 + -5n + -8 + 5n Reorder the terms: -8 + 5n + 3n2 = 8 + -8 + -5n + 5n Combine like terms: 8 + -8 = 0 -8 + 5n + 3n2 = 0 + -5n + 5n -8 + 5n + 3n2 = -5n + 5n Combine like terms: -5n + 5n = 0 -8 + 5n + 3n2 = 0 Factor a trinomial. (-8 + -3n)(1 + -1n) = 0Subproblem 1
Set the factor '(-8 + -3n)' equal to zero and attempt to solve: Simplifying -8 + -3n = 0 Solving -8 + -3n = 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 + -3n = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -3n = 0 + 8 -3n = 0 + 8 Combine like terms: 0 + 8 = 8 -3n = 8 Divide each side by '-3'. n = -2.666666667 Simplifying n = -2.666666667Subproblem 2
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 = 1Solution
n = {-2.666666667, 1}
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