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Simplifying (3n3 + -5n + n2) + -1(-8n2 + 3n3) = 0 Reorder the terms: (-5n + n2 + 3n3) + -1(-8n2 + 3n3) = 0 Remove parenthesis around (-5n + n2 + 3n3) -5n + n2 + 3n3 + -1(-8n2 + 3n3) = 0 -5n + n2 + 3n3 + (-8n2 * -1 + 3n3 * -1) = 0 -5n + n2 + 3n3 + (8n2 + -3n3) = 0 Reorder the terms: -5n + n2 + 8n2 + 3n3 + -3n3 = 0 Combine like terms: n2 + 8n2 = 9n2 -5n + 9n2 + 3n3 + -3n3 = 0 Combine like terms: 3n3 + -3n3 = 0 -5n + 9n2 + 0 = 0 -5n + 9n2 = 0 Solving -5n + 9n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), 'n'. n(-5 + 9n) = 0Subproblem 1
Set the factor 'n' equal to zero and attempt to solve: Simplifying n = 0 Solving n = 0 Move all terms containing n to the left, all other terms to the right. Simplifying n = 0Subproblem 2
Set the factor '(-5 + 9n)' equal to zero and attempt to solve: Simplifying -5 + 9n = 0 Solving -5 + 9n = 0 Move all terms containing n to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + 9n = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 9n = 0 + 5 9n = 0 + 5 Combine like terms: 0 + 5 = 5 9n = 5 Divide each side by '9'. n = 0.5555555556 Simplifying n = 0.5555555556Solution
n = {0, 0.5555555556}
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