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Simplifying -4n2 + -15n + -26 = -2 + -8n2 + 5n Reorder the terms: -26 + -15n + -4n2 = -2 + -8n2 + 5n Reorder the terms: -26 + -15n + -4n2 = -2 + 5n + -8n2 Solving -26 + -15n + -4n2 = -2 + 5n + -8n2 Solving for variable 'n'. Reorder the terms: -26 + 2 + -15n + -5n + -4n2 + 8n2 = -2 + 5n + -8n2 + 2 + -5n + 8n2 Combine like terms: -26 + 2 = -24 -24 + -15n + -5n + -4n2 + 8n2 = -2 + 5n + -8n2 + 2 + -5n + 8n2 Combine like terms: -15n + -5n = -20n -24 + -20n + -4n2 + 8n2 = -2 + 5n + -8n2 + 2 + -5n + 8n2 Combine like terms: -4n2 + 8n2 = 4n2 -24 + -20n + 4n2 = -2 + 5n + -8n2 + 2 + -5n + 8n2 Reorder the terms: -24 + -20n + 4n2 = -2 + 2 + 5n + -5n + -8n2 + 8n2 Combine like terms: -2 + 2 = 0 -24 + -20n + 4n2 = 0 + 5n + -5n + -8n2 + 8n2 -24 + -20n + 4n2 = 5n + -5n + -8n2 + 8n2 Combine like terms: 5n + -5n = 0 -24 + -20n + 4n2 = 0 + -8n2 + 8n2 -24 + -20n + 4n2 = -8n2 + 8n2 Combine like terms: -8n2 + 8n2 = 0 -24 + -20n + 4n2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-6 + -5n + n2) = 0 Factor a trinomial. 4((-1 + -1n)(6 + -1n)) = 0 Ignore the factor 4.Subproblem 1
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 = -1Subproblem 2
Set the factor '(6 + -1n)' equal to zero and attempt to solve: Simplifying 6 + -1n = 0 Solving 6 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1n = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1n = 0 + -6 -1n = 0 + -6 Combine like terms: 0 + -6 = -6 -1n = -6 Divide each side by '-1'. n = 6 Simplifying n = 6Solution
n = {-1, 6}
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