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Simplifying 4n2 + 2n = 2an + n2d + -1dn Reorder the terms: 2n + 4n2 = 2an + n2d + -1dn Reorder the terms: 2n + 4n2 = 2an + -1dn + dn2 Solving 2n + 4n2 = 2an + -1dn + dn2 Solving for variable 'n'. Reorder the terms: -2an + dn + -1dn2 + 2n + 4n2 = 2an + -1dn + dn2 + -2an + dn + -1dn2 Reorder the terms: -2an + dn + -1dn2 + 2n + 4n2 = 2an + -2an + -1dn + dn + dn2 + -1dn2 Combine like terms: 2an + -2an = 0 -2an + dn + -1dn2 + 2n + 4n2 = 0 + -1dn + dn + dn2 + -1dn2 -2an + dn + -1dn2 + 2n + 4n2 = -1dn + dn + dn2 + -1dn2 Combine like terms: -1dn + dn = 0 -2an + dn + -1dn2 + 2n + 4n2 = 0 + dn2 + -1dn2 -2an + dn + -1dn2 + 2n + 4n2 = dn2 + -1dn2 Combine like terms: dn2 + -1dn2 = 0 -2an + dn + -1dn2 + 2n + 4n2 = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(-2a + d + -1dn + 2 + 4n) = 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 '(-2a + d + -1dn + 2 + 4n)' equal to zero and attempt to solve: Simplifying -2a + d + -1dn + 2 + 4n = 0 Reorder the terms: 2 + -2a + d + -1dn + 4n = 0 Solving 2 + -2a + d + -1dn + 4n = 0 Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2a + d + -1dn + -2 + 4n = 0 + -2 Reorder the terms: 2 + -2 + -2a + d + -1dn + 4n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -2a + d + -1dn + 4n = 0 + -2 -2a + d + -1dn + 4n = 0 + -2 Combine like terms: 0 + -2 = -2 -2a + d + -1dn + 4n = -2 Add '2a' to each side of the equation. -2a + d + -1dn + 2a + 4n = -2 + 2a Reorder the terms: -2a + 2a + d + -1dn + 4n = -2 + 2a Combine like terms: -2a + 2a = 0 0 + d + -1dn + 4n = -2 + 2a d + -1dn + 4n = -2 + 2a Add '-1d' to each side of the equation. d + -1dn + -1d + 4n = -2 + 2a + -1d Reorder the terms: d + -1d + -1dn + 4n = -2 + 2a + -1d Combine like terms: d + -1d = 0 0 + -1dn + 4n = -2 + 2a + -1d -1dn + 4n = -2 + 2a + -1d The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
n = {0}
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