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Simplifying (2x + y)(3m + n) + -1(2x + y)(m + -3n) = 0 Multiply (2x + y) * (3m + n) (2x * (3m + n) + y(3m + n)) + -1(2x + y)(m + -3n) = 0 ((3m * 2x + n * 2x) + y(3m + n)) + -1(2x + y)(m + -3n) = 0 ((6mx + 2nx) + y(3m + n)) + -1(2x + y)(m + -3n) = 0 (6mx + 2nx + (3m * y + n * y)) + -1(2x + y)(m + -3n) = 0 (6mx + 2nx + (3my + ny)) + -1(2x + y)(m + -3n) = 0 Reorder the terms: (6mx + 3my + 2nx + ny) + -1(2x + y)(m + -3n) = 0 (6mx + 3my + 2nx + ny) + -1(2x + y)(m + -3n) = 0 Multiply (2x + y) * (m + -3n) 6mx + 3my + 2nx + ny + -1(2x * (m + -3n) + y(m + -3n)) = 0 6mx + 3my + 2nx + ny + -1((m * 2x + -3n * 2x) + y(m + -3n)) = 0 6mx + 3my + 2nx + ny + -1((2mx + -6nx) + y(m + -3n)) = 0 6mx + 3my + 2nx + ny + -1(2mx + -6nx + (m * y + -3n * y)) = 0 6mx + 3my + 2nx + ny + -1(2mx + -6nx + (my + -3ny)) = 0 Reorder the terms: 6mx + 3my + 2nx + ny + -1(2mx + my + -6nx + -3ny) = 0 6mx + 3my + 2nx + ny + -1(2mx + my + -6nx + -3ny) = 0 6mx + 3my + 2nx + ny + (2mx * -1 + my * -1 + -6nx * -1 + -3ny * -1) = 0 6mx + 3my + 2nx + ny + (-2mx + -1my + 6nx + 3ny) = 0 Reorder the terms: 6mx + -2mx + 3my + -1my + 2nx + 6nx + ny + 3ny = 0 Combine like terms: 6mx + -2mx = 4mx 4mx + 3my + -1my + 2nx + 6nx + ny + 3ny = 0 Combine like terms: 3my + -1my = 2my 4mx + 2my + 2nx + 6nx + ny + 3ny = 0 Combine like terms: 2nx + 6nx = 8nx 4mx + 2my + 8nx + ny + 3ny = 0 Combine like terms: ny + 3ny = 4ny 4mx + 2my + 8nx + 4ny = 0 Solving 4mx + 2my + 8nx + 4ny = 0 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-8nx' to each side of the equation. 4mx + 2my + 8nx + -8nx + 4ny = 0 + -8nx Combine like terms: 8nx + -8nx = 0 4mx + 2my + 0 + 4ny = 0 + -8nx 4mx + 2my + 4ny = 0 + -8nx Remove the zero: 4mx + 2my + 4ny = -8nx Add '-4ny' to each side of the equation. 4mx + 2my + 4ny + -4ny = -8nx + -4ny Combine like terms: 4ny + -4ny = 0 4mx + 2my + 0 = -8nx + -4ny 4mx + 2my = -8nx + -4ny Reorder the terms: 4mx + 2my + 8nx + 4ny = -8nx + 8nx + -4ny + 4ny Combine like terms: -8nx + 8nx = 0 4mx + 2my + 8nx + 4ny = 0 + -4ny + 4ny 4mx + 2my + 8nx + 4ny = -4ny + 4ny Combine like terms: -4ny + 4ny = 0 4mx + 2my + 8nx + 4ny = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(2mx + my + 4nx + 2ny) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2mx + my + 4nx + 2ny)' equal to zero and attempt to solve: Simplifying 2mx + my + 4nx + 2ny = 0 Solving 2mx + my + 4nx + 2ny = 0 Move all terms containing m to the left, all other terms to the right. Add '-4nx' to each side of the equation. 2mx + my + 4nx + -4nx + 2ny = 0 + -4nx Combine like terms: 4nx + -4nx = 0 2mx + my + 0 + 2ny = 0 + -4nx 2mx + my + 2ny = 0 + -4nx Remove the zero: 2mx + my + 2ny = -4nx Add '-2ny' to each side of the equation. 2mx + my + 2ny + -2ny = -4nx + -2ny Combine like terms: 2ny + -2ny = 0 2mx + my + 0 = -4nx + -2ny 2mx + my = -4nx + -2ny 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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