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Simplifying (2x + 4y + 3) * dy = (x + 2y + 1) * dx Reorder the terms: (3 + 2x + 4y) * dy = (x + 2y + 1) * dx Reorder the terms for easier multiplication: dy(3 + 2x + 4y) = (x + 2y + 1) * dx (3 * dy + 2x * dy + 4y * dy) = (x + 2y + 1) * dx Reorder the terms: (2dxy + 3dy + 4dy2) = (x + 2y + 1) * dx (2dxy + 3dy + 4dy2) = (x + 2y + 1) * dx Reorder the terms: 2dxy + 3dy + 4dy2 = (1 + x + 2y) * dx Reorder the terms for easier multiplication: 2dxy + 3dy + 4dy2 = dx(1 + x + 2y) 2dxy + 3dy + 4dy2 = (1 * dx + x * dx + 2y * dx) Reorder the terms: 2dxy + 3dy + 4dy2 = (1dx + 2dxy + dx2) 2dxy + 3dy + 4dy2 = (1dx + 2dxy + dx2) Add '-2dxy' to each side of the equation. 2dxy + 3dy + -2dxy + 4dy2 = 1dx + 2dxy + -2dxy + dx2 Reorder the terms: 2dxy + -2dxy + 3dy + 4dy2 = 1dx + 2dxy + -2dxy + dx2 Combine like terms: 2dxy + -2dxy = 0 0 + 3dy + 4dy2 = 1dx + 2dxy + -2dxy + dx2 3dy + 4dy2 = 1dx + 2dxy + -2dxy + dx2 Combine like terms: 2dxy + -2dxy = 0 3dy + 4dy2 = 1dx + 0 + dx2 3dy + 4dy2 = 1dx + dx2 Solving 3dy + 4dy2 = 1dx + dx2 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-1dx' to each side of the equation. 3dy + -1dx + 4dy2 = 1dx + -1dx + dx2 Reorder the terms: -1dx + 3dy + 4dy2 = 1dx + -1dx + dx2 Combine like terms: 1dx + -1dx = 0 -1dx + 3dy + 4dy2 = 0 + dx2 -1dx + 3dy + 4dy2 = dx2 Add '-1dx2' to each side of the equation. -1dx + 3dy + -1dx2 + 4dy2 = dx2 + -1dx2 Reorder the terms: -1dx + -1dx2 + 3dy + 4dy2 = dx2 + -1dx2 Combine like terms: dx2 + -1dx2 = 0 -1dx + -1dx2 + 3dy + 4dy2 = 0 Factor out the Greatest Common Factor (GCF), 'd'. d(-1x + -1x2 + 3y + 4y2) = 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 + -1x2 + 3y + 4y2)' equal to zero and attempt to solve: Simplifying -1x + -1x2 + 3y + 4y2 = 0 Solving -1x + -1x2 + 3y + 4y2 = 0 Move all terms containing d to the left, all other terms to the right. Add 'x' to each side of the equation. -1x + -1x2 + 3y + x + 4y2 = 0 + x Reorder the terms: -1x + x + -1x2 + 3y + 4y2 = 0 + x Combine like terms: -1x + x = 0 0 + -1x2 + 3y + 4y2 = 0 + x -1x2 + 3y + 4y2 = 0 + x Remove the zero: -1x2 + 3y + 4y2 = x Add 'x2' to each side of the equation. -1x2 + 3y + x2 + 4y2 = x + x2 Reorder the terms: -1x2 + x2 + 3y + 4y2 = x + x2 Combine like terms: -1x2 + x2 = 0 0 + 3y + 4y2 = x + x2 3y + 4y2 = x + x2 Add '-3y' to each side of the equation. 3y + -3y + 4y2 = x + x2 + -3y Combine like terms: 3y + -3y = 0 0 + 4y2 = x + x2 + -3y 4y2 = x + x2 + -3y Add '-4y2' to each side of the equation. 4y2 + -4y2 = x + x2 + -3y + -4y2 Combine like terms: 4y2 + -4y2 = 0 0 = x + x2 + -3y + -4y2 Simplifying 0 = x + x2 + -3y + -4y2 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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