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Simplifying 8n2 = 32n + 256 Reorder the terms: 8n2 = 256 + 32n Solving 8n2 = 256 + 32n Solving for variable 'n'. Reorder the terms: -256 + -32n + 8n2 = 256 + 32n + -256 + -32n Reorder the terms: -256 + -32n + 8n2 = 256 + -256 + 32n + -32n Combine like terms: 256 + -256 = 0 -256 + -32n + 8n2 = 0 + 32n + -32n -256 + -32n + 8n2 = 32n + -32n Combine like terms: 32n + -32n = 0 -256 + -32n + 8n2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-32 + -4n + n2) = 0 Factor a trinomial. 8((-4 + -1n)(8 + -1n)) = 0 Ignore the factor 8.Subproblem 1
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 = -4Subproblem 2
Set the factor '(8 + -1n)' equal to zero and attempt to solve: Simplifying 8 + -1n = 0 Solving 8 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1n = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1n = 0 + -8 -1n = 0 + -8 Combine like terms: 0 + -8 = -8 -1n = -8 Divide each side by '-1'. n = 8 Simplifying n = 8Solution
n = {-4, 8}
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