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Simplifying n2 + -4n + -18 = 3 Reorder the terms: -18 + -4n + n2 = 3 Solving -18 + -4n + n2 = 3 Solving for variable 'n'. Reorder the terms: -18 + -3 + -4n + n2 = 3 + -3 Combine like terms: -18 + -3 = -21 -21 + -4n + n2 = 3 + -3 Combine like terms: 3 + -3 = 0 -21 + -4n + n2 = 0 Factor a trinomial. (-3 + -1n)(7 + -1n) = 0Subproblem 1
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 = -3Subproblem 2
Set the factor '(7 + -1n)' equal to zero and attempt to solve: Simplifying 7 + -1n = 0 Solving 7 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1n = 0 + -7 -1n = 0 + -7 Combine like terms: 0 + -7 = -7 -1n = -7 Divide each side by '-1'. n = 7 Simplifying n = 7Solution
n = {-3, 7}
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