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Simplifying x(y2 + y + -2) * dx + (x + -4)(1 + 5y) * dy = 0 Reorder the terms: x(-2 + y + y2) * dx + (x + -4)(1 + 5y) * dy = 0 Reorder the terms for easier multiplication: x * dx(-2 + y + y2) + (x + -4)(1 + 5y) * dy = 0 Multiply x * dx dx2(-2 + y + y2) + (x + -4)(1 + 5y) * dy = 0 (-2 * dx2 + y * dx2 + y2 * dx2) + (x + -4)(1 + 5y) * dy = 0 (-2dx2 + dx2y + dx2y2) + (x + -4)(1 + 5y) * dy = 0 Reorder the terms: -2dx2 + dx2y + dx2y2 + (-4 + x)(1 + 5y) * dy = 0 Reorder the terms for easier multiplication: -2dx2 + dx2y + dx2y2 + dy(-4 + x)(1 + 5y) = 0 Multiply (-4 + x) * (1 + 5y) -2dx2 + dx2y + dx2y2 + dy(-4(1 + 5y) + x(1 + 5y)) = 0 -2dx2 + dx2y + dx2y2 + dy((1 * -4 + 5y * -4) + x(1 + 5y)) = 0 -2dx2 + dx2y + dx2y2 + dy((-4 + -20y) + x(1 + 5y)) = 0 -2dx2 + dx2y + dx2y2 + dy(-4 + -20y + (1 * x + 5y * x)) = 0 -2dx2 + dx2y + dx2y2 + dy(-4 + -20y + (1x + 5xy)) = 0 Reorder the terms: -2dx2 + dx2y + dx2y2 + dy(-4 + 1x + 5xy + -20y) = 0 -2dx2 + dx2y + dx2y2 + dy(-4 + 1x + 5xy + -20y) = 0 -2dx2 + dx2y + dx2y2 + (-4 * dy + 1x * dy + 5xy * dy + -20y * dy) = 0 Reorder the terms: -2dx2 + dx2y + dx2y2 + (1dxy + 5dxy2 + -4dy + -20dy2) = 0 -2dx2 + dx2y + dx2y2 + (1dxy + 5dxy2 + -4dy + -20dy2) = 0 Reorder the terms: 1dxy + 5dxy2 + -2dx2 + dx2y + dx2y2 + -4dy + -20dy2 = 0 Solving 1dxy + 5dxy2 + -2dx2 + dx2y + dx2y2 + -4dy + -20dy2 = 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(xy + 5xy2 + -2x2 + x2y + x2y2 + -4y + -20y2) = 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 '(xy + 5xy2 + -2x2 + x2y + x2y2 + -4y + -20y2)' equal to zero and attempt to solve: Simplifying xy + 5xy2 + -2x2 + x2y + x2y2 + -4y + -20y2 = 0 Solving xy + 5xy2 + -2x2 + x2y + x2y2 + -4y + -20y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-1xy' to each side of the equation. xy + 5xy2 + -2x2 + x2y + x2y2 + -4y + -1xy + -20y2 = 0 + -1xy Reorder the terms: xy + -1xy + 5xy2 + -2x2 + x2y + x2y2 + -4y + -20y2 = 0 + -1xy Combine like terms: xy + -1xy = 0 0 + 5xy2 + -2x2 + x2y + x2y2 + -4y + -20y2 = 0 + -1xy 5xy2 + -2x2 + x2y + x2y2 + -4y + -20y2 = 0 + -1xy Remove the zero: 5xy2 + -2x2 + x2y + x2y2 + -4y + -20y2 = -1xy Add '-5xy2' to each side of the equation. 5xy2 + -2x2 + x2y + x2y2 + -4y + -5xy2 + -20y2 = -1xy + -5xy2 Reorder the terms: 5xy2 + -5xy2 + -2x2 + x2y + x2y2 + -4y + -20y2 = -1xy + -5xy2 Combine like terms: 5xy2 + -5xy2 = 0 0 + -2x2 + x2y + x2y2 + -4y + -20y2 = -1xy + -5xy2 -2x2 + x2y + x2y2 + -4y + -20y2 = -1xy + -5xy2 Add '2x2' to each side of the equation. -2x2 + x2y + x2y2 + -4y + 2x2 + -20y2 = -1xy + -5xy2 + 2x2 Reorder the terms: -2x2 + 2x2 + x2y + x2y2 + -4y + -20y2 = -1xy + -5xy2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 0 + x2y + x2y2 + -4y + -20y2 = -1xy + -5xy2 + 2x2 x2y + x2y2 + -4y + -20y2 = -1xy + -5xy2 + 2x2 Add '-1x2y' to each side of the equation. x2y + x2y2 + -4y + -1x2y + -20y2 = -1xy + -5xy2 + 2x2 + -1x2y Reorder the terms: x2y + -1x2y + x2y2 + -4y + -20y2 = -1xy + -5xy2 + 2x2 + -1x2y Combine like terms: x2y + -1x2y = 0 0 + x2y2 + -4y + -20y2 = -1xy + -5xy2 + 2x2 + -1x2y x2y2 + -4y + -20y2 = -1xy + -5xy2 + 2x2 + -1x2y Add '-1x2y2' to each side of the equation. x2y2 + -4y + -1x2y2 + -20y2 = -1xy + -5xy2 + 2x2 + -1x2y + -1x2y2 Reorder the terms: x2y2 + -1x2y2 + -4y + -20y2 = -1xy + -5xy2 + 2x2 + -1x2y + -1x2y2 Combine like terms: x2y2 + -1x2y2 = 0 0 + -4y + -20y2 = -1xy + -5xy2 + 2x2 + -1x2y + -1x2y2 -4y + -20y2 = -1xy + -5xy2 + 2x2 + -1x2y + -1x2y2 Add '4y' to each side of the equation. -4y + 4y + -20y2 = -1xy + -5xy2 + 2x2 + -1x2y + -1x2y2 + 4y Combine like terms: -4y + 4y = 0 0 + -20y2 = -1xy + -5xy2 + 2x2 + -1x2y + -1x2y2 + 4y -20y2 = -1xy + -5xy2 + 2x2 + -1x2y + -1x2y2 + 4y Add '20y2' to each side of the equation. -20y2 + 20y2 = -1xy + -5xy2 + 2x2 + -1x2y + -1x2y2 + 4y + 20y2 Combine like terms: -20y2 + 20y2 = 0 0 = -1xy + -5xy2 + 2x2 + -1x2y + -1x2y2 + 4y + 20y2 Simplifying 0 = -1xy + -5xy2 + 2x2 + -1x2y + -1x2y2 + 4y + 20y2 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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