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Simplifying 2np + -6nq + -8n + -2 = -10p + -8 Reorder the terms: -2 + -8n + 2np + -6nq = -10p + -8 Reorder the terms: -2 + -8n + 2np + -6nq = -8 + -10p Solving -2 + -8n + 2np + -6nq = -8 + -10p Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2' to each side of the equation. -2 + -8n + 2np + 2 + -6nq = -8 + 2 + -10p Reorder the terms: -2 + 2 + -8n + 2np + -6nq = -8 + 2 + -10p Combine like terms: -2 + 2 = 0 0 + -8n + 2np + -6nq = -8 + 2 + -10p -8n + 2np + -6nq = -8 + 2 + -10p Combine like terms: -8 + 2 = -6 -8n + 2np + -6nq = -6 + -10p Reorder the terms: 6 + -8n + 2np + -6nq + 10p = -6 + -10p + 6 + 10p Reorder the terms: 6 + -8n + 2np + -6nq + 10p = -6 + 6 + -10p + 10p Combine like terms: -6 + 6 = 0 6 + -8n + 2np + -6nq + 10p = 0 + -10p + 10p 6 + -8n + 2np + -6nq + 10p = -10p + 10p Combine like terms: -10p + 10p = 0 6 + -8n + 2np + -6nq + 10p = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(3 + -4n + np + -3nq + 5p) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + -4n + np + -3nq + 5p)' equal to zero and attempt to solve: Simplifying 3 + -4n + np + -3nq + 5p = 0 Solving 3 + -4n + np + -3nq + 5p = 0 Move all terms containing n to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -4n + np + -3nq + -3 + 5p = 0 + -3 Reorder the terms: 3 + -3 + -4n + np + -3nq + 5p = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4n + np + -3nq + 5p = 0 + -3 -4n + np + -3nq + 5p = 0 + -3 Combine like terms: 0 + -3 = -3 -4n + np + -3nq + 5p = -3 Add '-5p' to each side of the equation. -4n + np + -3nq + 5p + -5p = -3 + -5p Combine like terms: 5p + -5p = 0 -4n + np + -3nq + 0 = -3 + -5p -4n + np + -3nq = -3 + -5p 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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