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Simplifying -3n(n + -3) + 4(n + 4) = 0 Reorder the terms: -3n(-3 + n) + 4(n + 4) = 0 (-3 * -3n + n * -3n) + 4(n + 4) = 0 (9n + -3n2) + 4(n + 4) = 0 Reorder the terms: 9n + -3n2 + 4(4 + n) = 0 9n + -3n2 + (4 * 4 + n * 4) = 0 9n + -3n2 + (16 + 4n) = 0 Reorder the terms: 16 + 9n + 4n + -3n2 = 0 Combine like terms: 9n + 4n = 13n 16 + 13n + -3n2 = 0 Solving 16 + 13n + -3n2 = 0 Solving for variable 'n'. Factor a trinomial. (16 + -3n)(1 + n) = 0Subproblem 1
Set the factor '(16 + -3n)' equal to zero and attempt to solve: Simplifying 16 + -3n = 0 Solving 16 + -3n = 0 Move all terms containing n to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + -3n = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -3n = 0 + -16 -3n = 0 + -16 Combine like terms: 0 + -16 = -16 -3n = -16 Divide each side by '-3'. n = 5.333333333 Simplifying n = 5.333333333Subproblem 2
Set the factor '(1 + n)' equal to zero and attempt to solve: Simplifying 1 + n = 0 Solving 1 + n = 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 + n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + n = 0 + -1 n = 0 + -1 Combine like terms: 0 + -1 = -1 n = -1 Simplifying n = -1Solution
n = {5.333333333, -1}
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