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Simplifying 6n2 + 8n + 8 = 5n2 + 1 Reorder the terms: 8 + 8n + 6n2 = 5n2 + 1 Reorder the terms: 8 + 8n + 6n2 = 1 + 5n2 Solving 8 + 8n + 6n2 = 1 + 5n2 Solving for variable 'n'. Reorder the terms: 8 + -1 + 8n + 6n2 + -5n2 = 1 + 5n2 + -1 + -5n2 Combine like terms: 8 + -1 = 7 7 + 8n + 6n2 + -5n2 = 1 + 5n2 + -1 + -5n2 Combine like terms: 6n2 + -5n2 = 1n2 7 + 8n + 1n2 = 1 + 5n2 + -1 + -5n2 Reorder the terms: 7 + 8n + 1n2 = 1 + -1 + 5n2 + -5n2 Combine like terms: 1 + -1 = 0 7 + 8n + 1n2 = 0 + 5n2 + -5n2 7 + 8n + 1n2 = 5n2 + -5n2 Combine like terms: 5n2 + -5n2 = 0 7 + 8n + 1n2 = 0 Factor a trinomial. (7 + n)(1 + n) = 0Subproblem 1
Set the factor '(7 + n)' equal to zero and attempt to solve: Simplifying 7 + n = 0 Solving 7 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + n = 0 + -7 n = 0 + -7 Combine like terms: 0 + -7 = -7 n = -7 Simplifying n = -7Subproblem 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 = {-7, -1}
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