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