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Simplifying (x + 4y3) * dx + -2(x2 + -1y) * dy = 0 Reorder the terms for easier multiplication: dx(x + 4y3) + -2(x2 + -1y) * dy = 0 (x * dx + 4y3 * dx) + -2(x2 + -1y) * dy = 0 Reorder the terms: (4dxy3 + dx2) + -2(x2 + -1y) * dy = 0 (4dxy3 + dx2) + -2(x2 + -1y) * dy = 0 Reorder the terms for easier multiplication: 4dxy3 + dx2 + -2dy(x2 + -1y) = 0 4dxy3 + dx2 + (x2 * -2dy + -1y * -2dy) = 0 4dxy3 + dx2 + (-2dx2y + 2dy2) = 0 Solving 4dxy3 + dx2 + -2dx2y + 2dy2 = 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(4xy3 + x2 + -2x2y + 2y2) = 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 '(4xy3 + x2 + -2x2y + 2y2)' equal to zero and attempt to solve: Simplifying 4xy3 + x2 + -2x2y + 2y2 = 0 Solving 4xy3 + x2 + -2x2y + 2y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-4xy3' to each side of the equation. 4xy3 + x2 + -2x2y + -4xy3 + 2y2 = 0 + -4xy3 Reorder the terms: 4xy3 + -4xy3 + x2 + -2x2y + 2y2 = 0 + -4xy3 Combine like terms: 4xy3 + -4xy3 = 0 0 + x2 + -2x2y + 2y2 = 0 + -4xy3 x2 + -2x2y + 2y2 = 0 + -4xy3 Remove the zero: x2 + -2x2y + 2y2 = -4xy3 Add '-1x2' to each side of the equation. x2 + -2x2y + -1x2 + 2y2 = -4xy3 + -1x2 Reorder the terms: x2 + -1x2 + -2x2y + 2y2 = -4xy3 + -1x2 Combine like terms: x2 + -1x2 = 0 0 + -2x2y + 2y2 = -4xy3 + -1x2 -2x2y + 2y2 = -4xy3 + -1x2 Add '2x2y' to each side of the equation. -2x2y + 2x2y + 2y2 = -4xy3 + -1x2 + 2x2y Combine like terms: -2x2y + 2x2y = 0 0 + 2y2 = -4xy3 + -1x2 + 2x2y 2y2 = -4xy3 + -1x2 + 2x2y Add '-2y2' to each side of the equation. 2y2 + -2y2 = -4xy3 + -1x2 + 2x2y + -2y2 Combine like terms: 2y2 + -2y2 = 0 0 = -4xy3 + -1x2 + 2x2y + -2y2 Simplifying 0 = -4xy3 + -1x2 + 2x2y + -2y2 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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