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Simplifying (5x + 3y + 1) * dx + (3xy + y + -4) * dy = 0 Reorder the terms: (1 + 5x + 3y) * dx + (3xy + y + -4) * dy = 0 Reorder the terms for easier multiplication: dx(1 + 5x + 3y) + (3xy + y + -4) * dy = 0 (1 * dx + 5x * dx + 3y * dx) + (3xy + y + -4) * dy = 0 Reorder the terms: (1dx + 3dxy + 5dx2) + (3xy + y + -4) * dy = 0 (1dx + 3dxy + 5dx2) + (3xy + y + -4) * dy = 0 Reorder the terms: 1dx + 3dxy + 5dx2 + (-4 + 3xy + y) * dy = 0 Reorder the terms for easier multiplication: 1dx + 3dxy + 5dx2 + dy(-4 + 3xy + y) = 0 1dx + 3dxy + 5dx2 + (-4 * dy + 3xy * dy + y * dy) = 0 Reorder the terms: 1dx + 3dxy + 5dx2 + (3dxy2 + -4dy + dy2) = 0 1dx + 3dxy + 5dx2 + (3dxy2 + -4dy + dy2) = 0 Reorder the terms: 1dx + 3dxy + 3dxy2 + 5dx2 + -4dy + dy2 = 0 Solving 1dx + 3dxy + 3dxy2 + 5dx2 + -4dy + dy2 = 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), 'd'. d(x + 3xy + 3xy2 + 5x2 + -4y + y2) = 0Subproblem 1
Set the factor 'd' equal to zero and attempt to solve: Simplifying d = 0 Solving d = 0 Move all terms containing d to the left, all other terms to the right. Simplifying d = 0Subproblem 2
Set the factor '(x + 3xy + 3xy2 + 5x2 + -4y + y2)' equal to zero and attempt to solve: Simplifying x + 3xy + 3xy2 + 5x2 + -4y + y2 = 0 Solving x + 3xy + 3xy2 + 5x2 + -4y + y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-1x' to each side of the equation. x + 3xy + 3xy2 + 5x2 + -4y + -1x + y2 = 0 + -1x Reorder the terms: x + -1x + 3xy + 3xy2 + 5x2 + -4y + y2 = 0 + -1x Combine like terms: x + -1x = 0 0 + 3xy + 3xy2 + 5x2 + -4y + y2 = 0 + -1x 3xy + 3xy2 + 5x2 + -4y + y2 = 0 + -1x Remove the zero: 3xy + 3xy2 + 5x2 + -4y + y2 = -1x Add '-3xy' to each side of the equation. 3xy + 3xy2 + 5x2 + -4y + -3xy + y2 = -1x + -3xy Reorder the terms: 3xy + -3xy + 3xy2 + 5x2 + -4y + y2 = -1x + -3xy Combine like terms: 3xy + -3xy = 0 0 + 3xy2 + 5x2 + -4y + y2 = -1x + -3xy 3xy2 + 5x2 + -4y + y2 = -1x + -3xy Add '-3xy2' to each side of the equation. 3xy2 + 5x2 + -4y + -3xy2 + y2 = -1x + -3xy + -3xy2 Reorder the terms: 3xy2 + -3xy2 + 5x2 + -4y + y2 = -1x + -3xy + -3xy2 Combine like terms: 3xy2 + -3xy2 = 0 0 + 5x2 + -4y + y2 = -1x + -3xy + -3xy2 5x2 + -4y + y2 = -1x + -3xy + -3xy2 Add '-5x2' to each side of the equation. 5x2 + -4y + -5x2 + y2 = -1x + -3xy + -3xy2 + -5x2 Reorder the terms: 5x2 + -5x2 + -4y + y2 = -1x + -3xy + -3xy2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 0 + -4y + y2 = -1x + -3xy + -3xy2 + -5x2 -4y + y2 = -1x + -3xy + -3xy2 + -5x2 Add '4y' to each side of the equation. -4y + 4y + y2 = -1x + -3xy + -3xy2 + -5x2 + 4y Combine like terms: -4y + 4y = 0 0 + y2 = -1x + -3xy + -3xy2 + -5x2 + 4y y2 = -1x + -3xy + -3xy2 + -5x2 + 4y Add '-1y2' to each side of the equation. y2 + -1y2 = -1x + -3xy + -3xy2 + -5x2 + 4y + -1y2 Combine like terms: y2 + -1y2 = 0 0 = -1x + -3xy + -3xy2 + -5x2 + 4y + -1y2 Simplifying 0 = -1x + -3xy + -3xy2 + -5x2 + 4y + -1y2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
d = {0}
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