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Simplifying 26n2 + -3n + -10 = 2 + n2 + -8n Reorder the terms: -10 + -3n + 26n2 = 2 + n2 + -8n Reorder the terms: -10 + -3n + 26n2 = 2 + -8n + n2 Solving -10 + -3n + 26n2 = 2 + -8n + n2 Solving for variable 'n'. Reorder the terms: -10 + -2 + -3n + 8n + 26n2 + -1n2 = 2 + -8n + n2 + -2 + 8n + -1n2 Combine like terms: -10 + -2 = -12 -12 + -3n + 8n + 26n2 + -1n2 = 2 + -8n + n2 + -2 + 8n + -1n2 Combine like terms: -3n + 8n = 5n -12 + 5n + 26n2 + -1n2 = 2 + -8n + n2 + -2 + 8n + -1n2 Combine like terms: 26n2 + -1n2 = 25n2 -12 + 5n + 25n2 = 2 + -8n + n2 + -2 + 8n + -1n2 Reorder the terms: -12 + 5n + 25n2 = 2 + -2 + -8n + 8n + n2 + -1n2 Combine like terms: 2 + -2 = 0 -12 + 5n + 25n2 = 0 + -8n + 8n + n2 + -1n2 -12 + 5n + 25n2 = -8n + 8n + n2 + -1n2 Combine like terms: -8n + 8n = 0 -12 + 5n + 25n2 = 0 + n2 + -1n2 -12 + 5n + 25n2 = n2 + -1n2 Combine like terms: n2 + -1n2 = 0 -12 + 5n + 25n2 = 0 Factor a trinomial. (-4 + -5n)(3 + -5n) = 0Subproblem 1
Set the factor '(-4 + -5n)' equal to zero and attempt to solve: Simplifying -4 + -5n = 0 Solving -4 + -5n = 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 + -5n = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -5n = 0 + 4 -5n = 0 + 4 Combine like terms: 0 + 4 = 4 -5n = 4 Divide each side by '-5'. n = -0.8 Simplifying n = -0.8Subproblem 2
Set the factor '(3 + -5n)' equal to zero and attempt to solve: Simplifying 3 + -5n = 0 Solving 3 + -5n = 0 Move all terms containing n to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -5n = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5n = 0 + -3 -5n = 0 + -3 Combine like terms: 0 + -3 = -3 -5n = -3 Divide each side by '-5'. n = 0.6 Simplifying n = 0.6Solution
n = {-0.8, 0.6}
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