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Simplifying bn(a + -3c + 5m) + -4an(6b + -2m) = 0 (a * bn + -3c * bn + 5m * bn) + -4an(6b + -2m) = 0 (abn + -3bcn + 5bmn) + -4an(6b + -2m) = 0 abn + -3bcn + 5bmn + (6b * -4an + -2m * -4an) = 0 abn + -3bcn + 5bmn + (-24abn + 8amn) = 0 Reorder the terms: abn + -24abn + 8amn + -3bcn + 5bmn = 0 Combine like terms: abn + -24abn = -23abn -23abn + 8amn + -3bcn + 5bmn = 0 Solving -23abn + 8amn + -3bcn + 5bmn = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3bcn' to each side of the equation. -23abn + 8amn + -3bcn + 3bcn + 5bmn = 0 + 3bcn Combine like terms: -3bcn + 3bcn = 0 -23abn + 8amn + 0 + 5bmn = 0 + 3bcn -23abn + 8amn + 5bmn = 0 + 3bcn Remove the zero: -23abn + 8amn + 5bmn = 3bcn Add '-5bmn' to each side of the equation. -23abn + 8amn + 5bmn + -5bmn = 3bcn + -5bmn Combine like terms: 5bmn + -5bmn = 0 -23abn + 8amn + 0 = 3bcn + -5bmn -23abn + 8amn = 3bcn + -5bmn Reorder the terms: -23abn + 8amn + -3bcn + 5bmn = 3bcn + -3bcn + -5bmn + 5bmn Combine like terms: 3bcn + -3bcn = 0 -23abn + 8amn + -3bcn + 5bmn = 0 + -5bmn + 5bmn -23abn + 8amn + -3bcn + 5bmn = -5bmn + 5bmn Combine like terms: -5bmn + 5bmn = 0 -23abn + 8amn + -3bcn + 5bmn = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(-23ab + 8am + -3bc + 5bm) = 0Subproblem 1
Set the factor 'n' equal to zero and attempt to solve: Simplifying n = 0 Solving n = 0 Move all terms containing a to the left, all other terms to the right. Add '-1n' to each side of the equation. n + -1n = 0 + -1n Remove the zero: 0 = -1n Simplifying 0 = -1n The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-23ab + 8am + -3bc + 5bm)' equal to zero and attempt to solve: Simplifying -23ab + 8am + -3bc + 5bm = 0 Solving -23ab + 8am + -3bc + 5bm = 0 Move all terms containing a to the left, all other terms to the right. Add '3bc' to each side of the equation. -23ab + 8am + -3bc + 3bc + 5bm = 0 + 3bc Combine like terms: -3bc + 3bc = 0 -23ab + 8am + 0 + 5bm = 0 + 3bc -23ab + 8am + 5bm = 0 + 3bc Remove the zero: -23ab + 8am + 5bm = 3bc Add '-5bm' to each side of the equation. -23ab + 8am + 5bm + -5bm = 3bc + -5bm Combine like terms: 5bm + -5bm = 0 -23ab + 8am + 0 = 3bc + -5bm -23ab + 8am = 3bc + -5bm The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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