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Simplifying -30 = -13n + n2 Solving -30 = -13n + n2 Solving for variable 'n'. Reorder the terms: -30 + 13n + -1n2 = -13n + 13n + n2 + -1n2 Combine like terms: -13n + 13n = 0 -30 + 13n + -1n2 = 0 + n2 + -1n2 -30 + 13n + -1n2 = n2 + -1n2 Combine like terms: n2 + -1n2 = 0 -30 + 13n + -1n2 = 0 Factor a trinomial. (-10 + n)(3 + -1n) = 0Subproblem 1
Set the factor '(-10 + n)' equal to zero and attempt to solve: Simplifying -10 + n = 0 Solving -10 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + n = 0 + 10 Combine like terms: -10 + 10 = 0 0 + n = 0 + 10 n = 0 + 10 Combine like terms: 0 + 10 = 10 n = 10 Simplifying n = 10Subproblem 2
Set the factor '(3 + -1n)' equal to zero and attempt to solve: Simplifying 3 + -1n = 0 Solving 3 + -1n = 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 + -1n = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1n = 0 + -3 -1n = 0 + -3 Combine like terms: 0 + -3 = -3 -1n = -3 Divide each side by '-1'. n = 3 Simplifying n = 3Solution
n = {10, 3}
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