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