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