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Simplifying 5n2 = -24n + 36 Reorder the terms: 5n2 = 36 + -24n Solving 5n2 = 36 + -24n Solving for variable 'n'. Reorder the terms: -36 + 24n + 5n2 = 36 + -24n + -36 + 24n Reorder the terms: -36 + 24n + 5n2 = 36 + -36 + -24n + 24n Combine like terms: 36 + -36 = 0 -36 + 24n + 5n2 = 0 + -24n + 24n -36 + 24n + 5n2 = -24n + 24n Combine like terms: -24n + 24n = 0 -36 + 24n + 5n2 = 0 Factor a trinomial. (-6 + -1n)(6 + -5n) = 0Subproblem 1
Set the factor '(-6 + -1n)' equal to zero and attempt to solve: Simplifying -6 + -1n = 0 Solving -6 + -1n = 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 + -1n = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1n = 0 + 6 -1n = 0 + 6 Combine like terms: 0 + 6 = 6 -1n = 6 Divide each side by '-1'. n = -6 Simplifying n = -6Subproblem 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 = {-6, 1.2}
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