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Simplifying 2n2 = -5n + 12 Reorder the terms: 2n2 = 12 + -5n Solving 2n2 = 12 + -5n Solving for variable 'n'. Reorder the terms: -12 + 5n + 2n2 = 12 + -5n + -12 + 5n Reorder the terms: -12 + 5n + 2n2 = 12 + -12 + -5n + 5n Combine like terms: 12 + -12 = 0 -12 + 5n + 2n2 = 0 + -5n + 5n -12 + 5n + 2n2 = -5n + 5n Combine like terms: -5n + 5n = 0 -12 + 5n + 2n2 = 0 Factor a trinomial. (-4 + -1n)(3 + -2n) = 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 + -2n)' equal to zero and attempt to solve: Simplifying 3 + -2n = 0 Solving 3 + -2n = 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 + -2n = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2n = 0 + -3 -2n = 0 + -3 Combine like terms: 0 + -3 = -3 -2n = -3 Divide each side by '-2'. n = 1.5 Simplifying n = 1.5Solution
n = {-4, 1.5}
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