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Simplifying (3x2 + -2x + -1y) * dx + (2y + -1x + 3y2) * dy = 0 Reorder the terms: (-2x + 3x2 + -1y) * dx + (2y + -1x + 3y2) * dy = 0 Reorder the terms for easier multiplication: dx(-2x + 3x2 + -1y) + (2y + -1x + 3y2) * dy = 0 (-2x * dx + 3x2 * dx + -1y * dx) + (2y + -1x + 3y2) * dy = 0 Reorder the terms: (-1dxy + -2dx2 + 3dx3) + (2y + -1x + 3y2) * dy = 0 (-1dxy + -2dx2 + 3dx3) + (2y + -1x + 3y2) * dy = 0 Reorder the terms: -1dxy + -2dx2 + 3dx3 + (-1x + 2y + 3y2) * dy = 0 Reorder the terms for easier multiplication: -1dxy + -2dx2 + 3dx3 + dy(-1x + 2y + 3y2) = 0 -1dxy + -2dx2 + 3dx3 + (-1x * dy + 2y * dy + 3y2 * dy) = 0 -1dxy + -2dx2 + 3dx3 + (-1dxy + 2dy2 + 3dy3) = 0 Reorder the terms: -1dxy + -1dxy + -2dx2 + 3dx3 + 2dy2 + 3dy3 = 0 Combine like terms: -1dxy + -1dxy = -2dxy -2dxy + -2dx2 + 3dx3 + 2dy2 + 3dy3 = 0 Solving -2dxy + -2dx2 + 3dx3 + 2dy2 + 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(-2xy + -2x2 + 3x3 + 2y2 + 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 '(-2xy + -2x2 + 3x3 + 2y2 + 3y3)' equal to zero and attempt to solve: Simplifying -2xy + -2x2 + 3x3 + 2y2 + 3y3 = 0 Solving -2xy + -2x2 + 3x3 + 2y2 + 3y3 = 0 Move all terms containing d to the left, all other terms to the right. Add '2xy' to each side of the equation. -2xy + -2x2 + 3x3 + 2y2 + 2xy + 3y3 = 0 + 2xy Reorder the terms: -2xy + 2xy + -2x2 + 3x3 + 2y2 + 3y3 = 0 + 2xy Combine like terms: -2xy + 2xy = 0 0 + -2x2 + 3x3 + 2y2 + 3y3 = 0 + 2xy -2x2 + 3x3 + 2y2 + 3y3 = 0 + 2xy Remove the zero: -2x2 + 3x3 + 2y2 + 3y3 = 2xy Add '2x2' to each side of the equation. -2x2 + 3x3 + 2y2 + 2x2 + 3y3 = 2xy + 2x2 Reorder the terms: -2x2 + 2x2 + 3x3 + 2y2 + 3y3 = 2xy + 2x2 Combine like terms: -2x2 + 2x2 = 0 0 + 3x3 + 2y2 + 3y3 = 2xy + 2x2 3x3 + 2y2 + 3y3 = 2xy + 2x2 Add '-3x3' to each side of the equation. 3x3 + 2y2 + -3x3 + 3y3 = 2xy + 2x2 + -3x3 Reorder the terms: 3x3 + -3x3 + 2y2 + 3y3 = 2xy + 2x2 + -3x3 Combine like terms: 3x3 + -3x3 = 0 0 + 2y2 + 3y3 = 2xy + 2x2 + -3x3 2y2 + 3y3 = 2xy + 2x2 + -3x3 Add '-2y2' to each side of the equation. 2y2 + -2y2 + 3y3 = 2xy + 2x2 + -3x3 + -2y2 Combine like terms: 2y2 + -2y2 = 0 0 + 3y3 = 2xy + 2x2 + -3x3 + -2y2 3y3 = 2xy + 2x2 + -3x3 + -2y2 Add '-3y3' to each side of the equation. 3y3 + -3y3 = 2xy + 2x2 + -3x3 + -2y2 + -3y3 Combine like terms: 3y3 + -3y3 = 0 0 = 2xy + 2x2 + -3x3 + -2y2 + -3y3 Simplifying 0 = 2xy + 2x2 + -3x3 + -2y2 + -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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