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Simplifying 5n2 = -4n + 12 Reorder the terms: 5n2 = 12 + -4n Solving 5n2 = 12 + -4n Solving for variable 'n'. Reorder the terms: -12 + 4n + 5n2 = 12 + -4n + -12 + 4n Reorder the terms: -12 + 4n + 5n2 = 12 + -12 + -4n + 4n Combine like terms: 12 + -12 = 0 -12 + 4n + 5n2 = 0 + -4n + 4n -12 + 4n + 5n2 = -4n + 4n Combine like terms: -4n + 4n = 0 -12 + 4n + 5n2 = 0 Factor a trinomial. (-2 + -1n)(6 + -5n) = 0Subproblem 1
Set the factor '(-2 + -1n)' equal to zero and attempt to solve: Simplifying -2 + -1n = 0 Solving -2 + -1n = 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 + -1n = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1n = 0 + 2 -1n = 0 + 2 Combine like terms: 0 + 2 = 2 -1n = 2 Divide each side by '-1'. n = -2 Simplifying n = -2Subproblem 2
Set the factor '(6 + -5n)' equal to zero and attempt to solve: Simplifying 6 + -5n = 0 Solving 6 + -5n = 0 Move all terms containing n to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -5n = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -5n = 0 + -6 -5n = 0 + -6 Combine like terms: 0 + -6 = -6 -5n = -6 Divide each side by '-5'. n = 1.2 Simplifying n = 1.2Solution
n = {-2, 1.2}
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