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Simplifying 2(x + y) + 6n(x + y) = 0 (x * 2 + y * 2) + 6n(x + y) = 0 (2x + 2y) + 6n(x + y) = 0 2x + 2y + (x * 6n + y * 6n) = 0 2x + 2y + (6nx + 6ny) = 0 Reorder the terms: 6nx + 6ny + 2x + 2y = 0 Solving 6nx + 6ny + 2x + 2y = 0 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2x' to each side of the equation. 6nx + 6ny + 2x + -2x + 2y = 0 + -2x Combine like terms: 2x + -2x = 0 6nx + 6ny + 0 + 2y = 0 + -2x 6nx + 6ny + 2y = 0 + -2x Remove the zero: 6nx + 6ny + 2y = -2x Add '-2y' to each side of the equation. 6nx + 6ny + 2y + -2y = -2x + -2y Combine like terms: 2y + -2y = 0 6nx + 6ny + 0 = -2x + -2y 6nx + 6ny = -2x + -2y Reorder the terms: 6nx + 6ny + 2x + 2y = -2x + 2x + -2y + 2y Combine like terms: -2x + 2x = 0 6nx + 6ny + 2x + 2y = 0 + -2y + 2y 6nx + 6ny + 2x + 2y = -2y + 2y Combine like terms: -2y + 2y = 0 6nx + 6ny + 2x + 2y = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(3nx + 3ny + x + y) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3nx + 3ny + x + y)' equal to zero and attempt to solve: Simplifying 3nx + 3ny + x + y = 0 Solving 3nx + 3ny + x + y = 0 Move all terms containing n to the left, all other terms to the right. Add '-1x' to each side of the equation. 3nx + 3ny + x + -1x + y = 0 + -1x Combine like terms: x + -1x = 0 3nx + 3ny + 0 + y = 0 + -1x 3nx + 3ny + y = 0 + -1x Remove the zero: 3nx + 3ny + y = -1x Add '-1y' to each side of the equation. 3nx + 3ny + y + -1y = -1x + -1y Combine like terms: y + -1y = 0 3nx + 3ny + 0 = -1x + -1y 3nx + 3ny = -1x + -1y 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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