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Simplifying (6x2 + 2y2) * dx + -1(x2 + 4xy) * dy = 0 Reorder the terms for easier multiplication: dx(6x2 + 2y2) + -1(x2 + 4xy) * dy = 0 (6x2 * dx + 2y2 * dx) + -1(x2 + 4xy) * dy = 0 Reorder the terms: (2dxy2 + 6dx3) + -1(x2 + 4xy) * dy = 0 (2dxy2 + 6dx3) + -1(x2 + 4xy) * dy = 0 Reorder the terms: 2dxy2 + 6dx3 + -1(4xy + x2) * dy = 0 Reorder the terms for easier multiplication: 2dxy2 + 6dx3 + -1dy(4xy + x2) = 0 2dxy2 + 6dx3 + (4xy * -1dy + x2 * -1dy) = 0 2dxy2 + 6dx3 + (-4dxy2 + -1dx2y) = 0 Reorder the terms: 2dxy2 + -4dxy2 + -1dx2y + 6dx3 = 0 Combine like terms: 2dxy2 + -4dxy2 = -2dxy2 -2dxy2 + -1dx2y + 6dx3 = 0 Solving -2dxy2 + -1dx2y + 6dx3 = 0 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), 'dx'. dx(-2y2 + -1xy + 6x2) = 0 Factor a trinomial. dx((-1y + -2x)(2y + -3x)) = 0Subproblem 1
Set the factor 'dx' equal to zero and attempt to solve: Simplifying dx = 0 Solving dx = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dx = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-1y + -2x)' equal to zero and attempt to solve: Simplifying -1y + -2x = 0 Reorder the terms: -2x + -1y = 0 Solving -2x + -1y = 0 Move all terms containing d to the left, all other terms to the right. Add '2x' to each side of the equation. -2x + 2x + -1y = 0 + 2x Combine like terms: -2x + 2x = 0 0 + -1y = 0 + 2x -1y = 0 + 2x Remove the zero: -1y = 2x Add 'y' to each side of the equation. -1y + y = 2x + y Combine like terms: -1y + y = 0 0 = 2x + y Simplifying 0 = 2x + y The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(2y + -3x)' equal to zero and attempt to solve: Simplifying 2y + -3x = 0 Reorder the terms: -3x + 2y = 0 Solving -3x + 2y = 0 Move all terms containing d to the left, all other terms to the right. Add '3x' to each side of the equation. -3x + 3x + 2y = 0 + 3x Combine like terms: -3x + 3x = 0 0 + 2y = 0 + 3x 2y = 0 + 3x Remove the zero: 2y = 3x Add '-2y' to each side of the equation. 2y + -2y = 3x + -2y Combine like terms: 2y + -2y = 0 0 = 3x + -2y Simplifying 0 = 3x + -2y 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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