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Simplifying (4x3y + y3 + -2x) * dx + (x4 + 3xy3 + -3y2) * dy = 0 Reorder the terms: (-2x + 4x3y + y3) * dx + (x4 + 3xy3 + -3y2) * dy = 0 Reorder the terms for easier multiplication: dx(-2x + 4x3y + y3) + (x4 + 3xy3 + -3y2) * dy = 0 (-2x * dx + 4x3y * dx + y3 * dx) + (x4 + 3xy3 + -3y2) * dy = 0 Reorder the terms: (dxy3 + -2dx2 + 4dx4y) + (x4 + 3xy3 + -3y2) * dy = 0 (dxy3 + -2dx2 + 4dx4y) + (x4 + 3xy3 + -3y2) * dy = 0 Reorder the terms: dxy3 + -2dx2 + 4dx4y + (3xy3 + x4 + -3y2) * dy = 0 Reorder the terms for easier multiplication: dxy3 + -2dx2 + 4dx4y + dy(3xy3 + x4 + -3y2) = 0 dxy3 + -2dx2 + 4dx4y + (3xy3 * dy + x4 * dy + -3y2 * dy) = 0 dxy3 + -2dx2 + 4dx4y + (3dxy4 + dx4y + -3dy3) = 0 Reorder the terms: dxy3 + 3dxy4 + -2dx2 + 4dx4y + dx4y + -3dy3 = 0 Combine like terms: 4dx4y + dx4y = 5dx4y dxy3 + 3dxy4 + -2dx2 + 5dx4y + -3dy3 = 0 Solving dxy3 + 3dxy4 + -2dx2 + 5dx4y + -3dy3 = 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(xy3 + 3xy4 + -2x2 + 5x4y + -3y3) = 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 '(xy3 + 3xy4 + -2x2 + 5x4y + -3y3)' equal to zero and attempt to solve: Simplifying xy3 + 3xy4 + -2x2 + 5x4y + -3y3 = 0 Solving xy3 + 3xy4 + -2x2 + 5x4y + -3y3 = 0 Move all terms containing d to the left, all other terms to the right. Add '-1xy3' to each side of the equation. xy3 + 3xy4 + -2x2 + 5x4y + -1xy3 + -3y3 = 0 + -1xy3 Reorder the terms: xy3 + -1xy3 + 3xy4 + -2x2 + 5x4y + -3y3 = 0 + -1xy3 Combine like terms: xy3 + -1xy3 = 0 0 + 3xy4 + -2x2 + 5x4y + -3y3 = 0 + -1xy3 3xy4 + -2x2 + 5x4y + -3y3 = 0 + -1xy3 Remove the zero: 3xy4 + -2x2 + 5x4y + -3y3 = -1xy3 Add '-3xy4' to each side of the equation. 3xy4 + -2x2 + 5x4y + -3xy4 + -3y3 = -1xy3 + -3xy4 Reorder the terms: 3xy4 + -3xy4 + -2x2 + 5x4y + -3y3 = -1xy3 + -3xy4 Combine like terms: 3xy4 + -3xy4 = 0 0 + -2x2 + 5x4y + -3y3 = -1xy3 + -3xy4 -2x2 + 5x4y + -3y3 = -1xy3 + -3xy4 Add '2x2' to each side of the equation. -2x2 + 5x4y + 2x2 + -3y3 = -1xy3 + -3xy4 + 2x2 Reorder the terms: -2x2 + 2x2 + 5x4y + -3y3 = -1xy3 + -3xy4 + 2x2 Combine like terms: -2x2 + 2x2 = 0 0 + 5x4y + -3y3 = -1xy3 + -3xy4 + 2x2 5x4y + -3y3 = -1xy3 + -3xy4 + 2x2 Add '-5x4y' to each side of the equation. 5x4y + -5x4y + -3y3 = -1xy3 + -3xy4 + 2x2 + -5x4y Combine like terms: 5x4y + -5x4y = 0 0 + -3y3 = -1xy3 + -3xy4 + 2x2 + -5x4y -3y3 = -1xy3 + -3xy4 + 2x2 + -5x4y Add '3y3' to each side of the equation. -3y3 + 3y3 = -1xy3 + -3xy4 + 2x2 + -5x4y + 3y3 Combine like terms: -3y3 + 3y3 = 0 0 = -1xy3 + -3xy4 + 2x2 + -5x4y + 3y3 Simplifying 0 = -1xy3 + -3xy4 + 2x2 + -5x4y + 3y3 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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