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