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Simplifying 1 = (4n2 + 12n + -72) + -1(n + -4) Reorder the terms: 1 = (-72 + 12n + 4n2) + -1(n + -4) Remove parenthesis around (-72 + 12n + 4n2) 1 = -72 + 12n + 4n2 + -1(n + -4) Reorder the terms: 1 = -72 + 12n + 4n2 + -1(-4 + n) 1 = -72 + 12n + 4n2 + (-4 * -1 + n * -1) 1 = -72 + 12n + 4n2 + (4 + -1n) Reorder the terms: 1 = -72 + 4 + 12n + -1n + 4n2 Combine like terms: -72 + 4 = -68 1 = -68 + 12n + -1n + 4n2 Combine like terms: 12n + -1n = 11n 1 = -68 + 11n + 4n2 Solving 1 = -68 + 11n + 4n2 Solving for variable 'n'. Combine like terms: 1 + 68 = 69 69 + -11n + -4n2 = -68 + 11n + 4n2 + 68 + -11n + -4n2 Reorder the terms: 69 + -11n + -4n2 = -68 + 68 + 11n + -11n + 4n2 + -4n2 Combine like terms: -68 + 68 = 0 69 + -11n + -4n2 = 0 + 11n + -11n + 4n2 + -4n2 69 + -11n + -4n2 = 11n + -11n + 4n2 + -4n2 Combine like terms: 11n + -11n = 0 69 + -11n + -4n2 = 0 + 4n2 + -4n2 69 + -11n + -4n2 = 4n2 + -4n2 Combine like terms: 4n2 + -4n2 = 0 69 + -11n + -4n2 = 0 Factor a trinomial. (3 + -1n)(23 + 4n) = 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 '(23 + 4n)' equal to zero and attempt to solve: Simplifying 23 + 4n = 0 Solving 23 + 4n = 0 Move all terms containing n to the left, all other terms to the right. Add '-23' to each side of the equation. 23 + -23 + 4n = 0 + -23 Combine like terms: 23 + -23 = 0 0 + 4n = 0 + -23 4n = 0 + -23 Combine like terms: 0 + -23 = -23 4n = -23 Divide each side by '4'. n = -5.75 Simplifying n = -5.75Solution
n = {3, -5.75}
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