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Simplifying 2 = n2 + -7n + 12 Reorder the terms: 2 = 12 + -7n + n2 Solving 2 = 12 + -7n + n2 Solving for variable 'n'. Combine like terms: 2 + -12 = -10 -10 + 7n + -1n2 = 12 + -7n + n2 + -12 + 7n + -1n2 Reorder the terms: -10 + 7n + -1n2 = 12 + -12 + -7n + 7n + n2 + -1n2 Combine like terms: 12 + -12 = 0 -10 + 7n + -1n2 = 0 + -7n + 7n + n2 + -1n2 -10 + 7n + -1n2 = -7n + 7n + n2 + -1n2 Combine like terms: -7n + 7n = 0 -10 + 7n + -1n2 = 0 + n2 + -1n2 -10 + 7n + -1n2 = n2 + -1n2 Combine like terms: n2 + -1n2 = 0 -10 + 7n + -1n2 = 0 Factor a trinomial. (-5 + n)(2 + -1n) = 0Subproblem 1
Set the factor '(-5 + n)' equal to zero and attempt to solve: Simplifying -5 + n = 0 Solving -5 + n = 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 + n = 0 + 5 Combine like terms: -5 + 5 = 0 0 + n = 0 + 5 n = 0 + 5 Combine like terms: 0 + 5 = 5 n = 5 Simplifying n = 5Subproblem 2
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 = 2Solution
n = {5, 2}
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