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Simplifying 0 = 4n2 + n Reorder the terms: 0 = n + 4n2 Solving 0 = n + 4n2 Solving for variable 'n'. Remove the zero: -1n + -4n2 = n + 4n2 + -1n + -4n2 Reorder the terms: -1n + -4n2 = n + -1n + 4n2 + -4n2 Combine like terms: n + -1n = 0 -1n + -4n2 = 0 + 4n2 + -4n2 -1n + -4n2 = 4n2 + -4n2 Combine like terms: 4n2 + -4n2 = 0 -1n + -4n2 = 0 Factor out the Greatest Common Factor (GCF), '-1n'. -1n(1 + 4n) = 0 Ignore the factor -1.Subproblem 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 '(1 + 4n)' equal to zero and attempt to solve: Simplifying 1 + 4n = 0 Solving 1 + 4n = 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 + 4n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4n = 0 + -1 4n = 0 + -1 Combine like terms: 0 + -1 = -1 4n = -1 Divide each side by '4'. n = -0.25 Simplifying n = -0.25Solution
n = {0, -0.25}
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