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Simplifying 4x(3m + -4n) + -6y(3m + -4n) = 0 (3m * 4x + -4n * 4x) + -6y(3m + -4n) = 0 (12mx + -16nx) + -6y(3m + -4n) = 0 12mx + -16nx + (3m * -6y + -4n * -6y) = 0 12mx + -16nx + (-18my + 24ny) = 0 Reorder the terms: 12mx + -18my + -16nx + 24ny = 0 Solving 12mx + -18my + -16nx + 24ny = 0 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '16nx' to each side of the equation. 12mx + -18my + -16nx + 16nx + 24ny = 0 + 16nx Combine like terms: -16nx + 16nx = 0 12mx + -18my + 0 + 24ny = 0 + 16nx 12mx + -18my + 24ny = 0 + 16nx Remove the zero: 12mx + -18my + 24ny = 16nx Add '-24ny' to each side of the equation. 12mx + -18my + 24ny + -24ny = 16nx + -24ny Combine like terms: 24ny + -24ny = 0 12mx + -18my + 0 = 16nx + -24ny 12mx + -18my = 16nx + -24ny Reorder the terms: 12mx + -18my + -16nx + 24ny = 16nx + -16nx + -24ny + 24ny Combine like terms: 16nx + -16nx = 0 12mx + -18my + -16nx + 24ny = 0 + -24ny + 24ny 12mx + -18my + -16nx + 24ny = -24ny + 24ny Combine like terms: -24ny + 24ny = 0 12mx + -18my + -16nx + 24ny = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(6mx + -9my + -8nx + 12ny) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(6mx + -9my + -8nx + 12ny)' equal to zero and attempt to solve: Simplifying 6mx + -9my + -8nx + 12ny = 0 Solving 6mx + -9my + -8nx + 12ny = 0 Move all terms containing m to the left, all other terms to the right. Add '8nx' to each side of the equation. 6mx + -9my + -8nx + 8nx + 12ny = 0 + 8nx Combine like terms: -8nx + 8nx = 0 6mx + -9my + 0 + 12ny = 0 + 8nx 6mx + -9my + 12ny = 0 + 8nx Remove the zero: 6mx + -9my + 12ny = 8nx Add '-12ny' to each side of the equation. 6mx + -9my + 12ny + -12ny = 8nx + -12ny Combine like terms: 12ny + -12ny = 0 6mx + -9my + 0 = 8nx + -12ny 6mx + -9my = 8nx + -12ny 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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