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Simplifying n(n + 2) + -3(n + 4) = 0 Reorder the terms: n(2 + n) + -3(n + 4) = 0 (2 * n + n * n) + -3(n + 4) = 0 (2n + n2) + -3(n + 4) = 0 Reorder the terms: 2n + n2 + -3(4 + n) = 0 2n + n2 + (4 * -3 + n * -3) = 0 2n + n2 + (-12 + -3n) = 0 Reorder the terms: -12 + 2n + -3n + n2 = 0 Combine like terms: 2n + -3n = -1n -12 + -1n + n2 = 0 Solving -12 + -1n + n2 = 0 Solving for variable 'n'. Factor a trinomial. (-3 + -1n)(4 + -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 '(4 + -1n)' equal to zero and attempt to solve: Simplifying 4 + -1n = 0 Solving 4 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1n = 0 + -4 -1n = 0 + -4 Combine like terms: 0 + -4 = -4 -1n = -4 Divide each side by '-1'. n = 4 Simplifying n = 4Solution
n = {-3, 4}
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