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Simplifying 7n2 + -10n + -5 = -6n + 6n2 Reorder the terms: -5 + -10n + 7n2 = -6n + 6n2 Solving -5 + -10n + 7n2 = -6n + 6n2 Solving for variable 'n'. Reorder the terms: -5 + -10n + 6n + 7n2 + -6n2 = -6n + 6n2 + 6n + -6n2 Combine like terms: -10n + 6n = -4n -5 + -4n + 7n2 + -6n2 = -6n + 6n2 + 6n + -6n2 Combine like terms: 7n2 + -6n2 = 1n2 -5 + -4n + 1n2 = -6n + 6n2 + 6n + -6n2 Reorder the terms: -5 + -4n + 1n2 = -6n + 6n + 6n2 + -6n2 Combine like terms: -6n + 6n = 0 -5 + -4n + 1n2 = 0 + 6n2 + -6n2 -5 + -4n + 1n2 = 6n2 + -6n2 Combine like terms: 6n2 + -6n2 = 0 -5 + -4n + 1n2 = 0 Factor a trinomial. (-1 + -1n)(5 + -1n) = 0Subproblem 1
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 = -1Subproblem 2
Set the factor '(5 + -1n)' equal to zero and attempt to solve: Simplifying 5 + -1n = 0 Solving 5 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1n = 0 + -5 -1n = 0 + -5 Combine like terms: 0 + -5 = -5 -1n = -5 Divide each side by '-1'. n = 5 Simplifying n = 5Solution
n = {-1, 5}
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