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Simplifying 2n(n + 4) = n2 + 9 Reorder the terms: 2n(4 + n) = n2 + 9 (4 * 2n + n * 2n) = n2 + 9 (8n + 2n2) = n2 + 9 Reorder the terms: 8n + 2n2 = 9 + n2 Solving 8n + 2n2 = 9 + n2 Solving for variable 'n'. Reorder the terms: -9 + 8n + 2n2 + -1n2 = 9 + n2 + -9 + -1n2 Combine like terms: 2n2 + -1n2 = 1n2 -9 + 8n + 1n2 = 9 + n2 + -9 + -1n2 Reorder the terms: -9 + 8n + 1n2 = 9 + -9 + n2 + -1n2 Combine like terms: 9 + -9 = 0 -9 + 8n + 1n2 = 0 + n2 + -1n2 -9 + 8n + 1n2 = n2 + -1n2 Combine like terms: n2 + -1n2 = 0 -9 + 8n + 1n2 = 0 Factor a trinomial. (-9 + -1n)(1 + -1n) = 0Subproblem 1
Set the factor '(-9 + -1n)' equal to zero and attempt to solve: Simplifying -9 + -1n = 0 Solving -9 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1n = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1n = 0 + 9 -1n = 0 + 9 Combine like terms: 0 + 9 = 9 -1n = 9 Divide each side by '-1'. n = -9 Simplifying n = -9Subproblem 2
Set the factor '(1 + -1n)' equal to zero and attempt to solve: Simplifying 1 + -1n = 0 Solving 1 + -1n = 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 + -1n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1n = 0 + -1 -1n = 0 + -1 Combine like terms: 0 + -1 = -1 -1n = -1 Divide each side by '-1'. n = 1 Simplifying n = 1Solution
n = {-9, 1}
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