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Simplifying 2n2 = 8 + -15n Solving 2n2 = 8 + -15n Solving for variable 'n'. Reorder the terms: -8 + 15n + 2n2 = 8 + -15n + -8 + 15n Reorder the terms: -8 + 15n + 2n2 = 8 + -8 + -15n + 15n Combine like terms: 8 + -8 = 0 -8 + 15n + 2n2 = 0 + -15n + 15n -8 + 15n + 2n2 = -15n + 15n Combine like terms: -15n + 15n = 0 -8 + 15n + 2n2 = 0 Factor a trinomial. (-8 + -1n)(1 + -2n) = 0Subproblem 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 '(1 + -2n)' equal to zero and attempt to solve: Simplifying 1 + -2n = 0 Solving 1 + -2n = 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 + -2n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2n = 0 + -1 -2n = 0 + -1 Combine like terms: 0 + -1 = -1 -2n = -1 Divide each side by '-2'. n = 0.5 Simplifying n = 0.5Solution
n = {-8, 0.5}
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