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Simplifying (4x3 + 4xy + -1) * dx = (1 + -2x2 + -2y) * dy Reorder the terms: (-1 + 4xy + 4x3) * dx = (1 + -2x2 + -2y) * dy Reorder the terms for easier multiplication: dx(-1 + 4xy + 4x3) = (1 + -2x2 + -2y) * dy (-1 * dx + 4xy * dx + 4x3 * dx) = (1 + -2x2 + -2y) * dy (-1dx + 4dx2y + 4dx4) = (1 + -2x2 + -2y) * dy Reorder the terms for easier multiplication: -1dx + 4dx2y + 4dx4 = dy(1 + -2x2 + -2y) -1dx + 4dx2y + 4dx4 = (1 * dy + -2x2 * dy + -2y * dy) Reorder the terms: -1dx + 4dx2y + 4dx4 = (-2dx2y + 1dy + -2dy2) -1dx + 4dx2y + 4dx4 = (-2dx2y + 1dy + -2dy2) Solving -1dx + 4dx2y + 4dx4 = -2dx2y + 1dy + -2dy2 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '2dx2y' to each side of the equation. -1dx + 4dx2y + 2dx2y + 4dx4 = -2dx2y + 1dy + 2dx2y + -2dy2 Combine like terms: 4dx2y + 2dx2y = 6dx2y -1dx + 6dx2y + 4dx4 = -2dx2y + 1dy + 2dx2y + -2dy2 Reorder the terms: -1dx + 6dx2y + 4dx4 = -2dx2y + 2dx2y + 1dy + -2dy2 Combine like terms: -2dx2y + 2dx2y = 0 -1dx + 6dx2y + 4dx4 = 0 + 1dy + -2dy2 -1dx + 6dx2y + 4dx4 = 1dy + -2dy2 Add '-1dy' to each side of the equation. -1dx + 6dx2y + 4dx4 + -1dy = 1dy + -1dy + -2dy2 Combine like terms: 1dy + -1dy = 0 -1dx + 6dx2y + 4dx4 + -1dy = 0 + -2dy2 -1dx + 6dx2y + 4dx4 + -1dy = -2dy2 Add '2dy2' to each side of the equation. -1dx + 6dx2y + 4dx4 + -1dy + 2dy2 = -2dy2 + 2dy2 Combine like terms: -2dy2 + 2dy2 = 0 -1dx + 6dx2y + 4dx4 + -1dy + 2dy2 = 0 Factor out the Greatest Common Factor (GCF), 'd'. d(-1x + 6x2y + 4x4 + -1y + 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 '(-1x + 6x2y + 4x4 + -1y + 2y2)' equal to zero and attempt to solve: Simplifying -1x + 6x2y + 4x4 + -1y + 2y2 = 0 Solving -1x + 6x2y + 4x4 + -1y + 2y2 = 0 Move all terms containing d to the left, all other terms to the right. Add 'x' to each side of the equation. -1x + 6x2y + 4x4 + -1y + x + 2y2 = 0 + x Reorder the terms: -1x + x + 6x2y + 4x4 + -1y + 2y2 = 0 + x Combine like terms: -1x + x = 0 0 + 6x2y + 4x4 + -1y + 2y2 = 0 + x 6x2y + 4x4 + -1y + 2y2 = 0 + x Remove the zero: 6x2y + 4x4 + -1y + 2y2 = x Add '-6x2y' to each side of the equation. 6x2y + 4x4 + -1y + -6x2y + 2y2 = x + -6x2y Reorder the terms: 6x2y + -6x2y + 4x4 + -1y + 2y2 = x + -6x2y Combine like terms: 6x2y + -6x2y = 0 0 + 4x4 + -1y + 2y2 = x + -6x2y 4x4 + -1y + 2y2 = x + -6x2y Add '-4x4' to each side of the equation. 4x4 + -1y + -4x4 + 2y2 = x + -6x2y + -4x4 Reorder the terms: 4x4 + -4x4 + -1y + 2y2 = x + -6x2y + -4x4 Combine like terms: 4x4 + -4x4 = 0 0 + -1y + 2y2 = x + -6x2y + -4x4 -1y + 2y2 = x + -6x2y + -4x4 Add 'y' to each side of the equation. -1y + y + 2y2 = x + -6x2y + -4x4 + y Combine like terms: -1y + y = 0 0 + 2y2 = x + -6x2y + -4x4 + y 2y2 = x + -6x2y + -4x4 + y Add '-2y2' to each side of the equation. 2y2 + -2y2 = x + -6x2y + -4x4 + y + -2y2 Combine like terms: 2y2 + -2y2 = 0 0 = x + -6x2y + -4x4 + y + -2y2 Simplifying 0 = x + -6x2y + -4x4 + y + -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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