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Simplifying 2(a + b) + 8n(a + b) = 0 (a * 2 + b * 2) + 8n(a + b) = 0 (2a + 2b) + 8n(a + b) = 0 2a + 2b + (a * 8n + b * 8n) = 0 2a + 2b + (8an + 8bn) = 0 Reorder the terms: 2a + 8an + 2b + 8bn = 0 Solving 2a + 8an + 2b + 8bn = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2b' to each side of the equation. 2a + 8an + 2b + -2b + 8bn = 0 + -2b Combine like terms: 2b + -2b = 0 2a + 8an + 0 + 8bn = 0 + -2b 2a + 8an + 8bn = 0 + -2b Remove the zero: 2a + 8an + 8bn = -2b Add '-8bn' to each side of the equation. 2a + 8an + 8bn + -8bn = -2b + -8bn Combine like terms: 8bn + -8bn = 0 2a + 8an + 0 = -2b + -8bn 2a + 8an = -2b + -8bn Reorder the terms: 2a + 8an + 2b + 8bn = -2b + 2b + -8bn + 8bn Combine like terms: -2b + 2b = 0 2a + 8an + 2b + 8bn = 0 + -8bn + 8bn 2a + 8an + 2b + 8bn = -8bn + 8bn Combine like terms: -8bn + 8bn = 0 2a + 8an + 2b + 8bn = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(a + 4an + b + 4bn) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(a + 4an + b + 4bn)' equal to zero and attempt to solve: Simplifying a + 4an + b + 4bn = 0 Solving a + 4an + b + 4bn = 0 Move all terms containing a to the left, all other terms to the right. Add '-1b' to each side of the equation. a + 4an + b + -1b + 4bn = 0 + -1b Combine like terms: b + -1b = 0 a + 4an + 0 + 4bn = 0 + -1b a + 4an + 4bn = 0 + -1b Remove the zero: a + 4an + 4bn = -1b Add '-4bn' to each side of the equation. a + 4an + 4bn + -4bn = -1b + -4bn Combine like terms: 4bn + -4bn = 0 a + 4an + 0 = -1b + -4bn a + 4an = -1b + -4bn 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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