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Simplifying 5400 = n(8 + 2n) 5400 = (8 * n + 2n * n) 5400 = (8n + 2n2) Solving 5400 = 8n + 2n2 Solving for variable 'n'. Reorder the terms: 5400 + -8n + -2n2 = 8n + -8n + 2n2 + -2n2 Combine like terms: 8n + -8n = 0 5400 + -8n + -2n2 = 0 + 2n2 + -2n2 5400 + -8n + -2n2 = 2n2 + -2n2 Combine like terms: 2n2 + -2n2 = 0 5400 + -8n + -2n2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(2700 + -4n + -1n2) = 0 Factor a trinomial. 2((50 + -1n)(54 + n)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(50 + -1n)' equal to zero and attempt to solve: Simplifying 50 + -1n = 0 Solving 50 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + -1n = 0 + -50 Combine like terms: 50 + -50 = 0 0 + -1n = 0 + -50 -1n = 0 + -50 Combine like terms: 0 + -50 = -50 -1n = -50 Divide each side by '-1'. n = 50 Simplifying n = 50Subproblem 2
Set the factor '(54 + n)' equal to zero and attempt to solve: Simplifying 54 + n = 0 Solving 54 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '-54' to each side of the equation. 54 + -54 + n = 0 + -54 Combine like terms: 54 + -54 = 0 0 + n = 0 + -54 n = 0 + -54 Combine like terms: 0 + -54 = -54 n = -54 Simplifying n = -54Solution
n = {50, -54}
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