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Simplifying (n + 4) + n(n + 2) + n = 0 Reorder the terms: (4 + n) + n(n + 2) + n = 0 Remove parenthesis around (4 + n) 4 + n + n(n + 2) + n = 0 Reorder the terms: 4 + n + n(2 + n) + n = 0 4 + n + (2 * n + n * n) + n = 0 4 + n + (2n + n2) + n = 0 Reorder the terms: 4 + n + 2n + n + n2 = 0 Combine like terms: n + 2n = 3n 4 + 3n + n + n2 = 0 Combine like terms: 3n + n = 4n 4 + 4n + n2 = 0 Solving 4 + 4n + n2 = 0 Solving for variable 'n'. Factor a trinomial. (2 + n)(2 + n) = 0Subproblem 1
Set the factor '(2 + n)' equal to zero and attempt to solve: Simplifying 2 + n = 0 Solving 2 + n = 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 + n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + n = 0 + -2 n = 0 + -2 Combine like terms: 0 + -2 = -2 n = -2 Simplifying n = -2Subproblem 2
Set the factor '(2 + n)' equal to zero and attempt to solve: Simplifying 2 + n = 0 Solving 2 + n = 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 + n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + n = 0 + -2 n = 0 + -2 Combine like terms: 0 + -2 = -2 n = -2 Simplifying n = -2Solution
n = {-2, -2}
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