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Simplifying (3x + -2y + -5) * dx + -1(2x + 3y + 1) * dy = 0 Reorder the terms: (-5 + 3x + -2y) * dx + -1(2x + 3y + 1) * dy = 0 Reorder the terms for easier multiplication: dx(-5 + 3x + -2y) + -1(2x + 3y + 1) * dy = 0 (-5 * dx + 3x * dx + -2y * dx) + -1(2x + 3y + 1) * dy = 0 Reorder the terms: (-5dx + -2dxy + 3dx2) + -1(2x + 3y + 1) * dy = 0 (-5dx + -2dxy + 3dx2) + -1(2x + 3y + 1) * dy = 0 Reorder the terms: -5dx + -2dxy + 3dx2 + -1(1 + 2x + 3y) * dy = 0 Reorder the terms for easier multiplication: -5dx + -2dxy + 3dx2 + -1dy(1 + 2x + 3y) = 0 -5dx + -2dxy + 3dx2 + (1 * -1dy + 2x * -1dy + 3y * -1dy) = 0 Reorder the terms: -5dx + -2dxy + 3dx2 + (-2dxy + -1dy + -3dy2) = 0 -5dx + -2dxy + 3dx2 + (-2dxy + -1dy + -3dy2) = 0 Reorder the terms: -5dx + -2dxy + -2dxy + 3dx2 + -1dy + -3dy2 = 0 Combine like terms: -2dxy + -2dxy = -4dxy -5dx + -4dxy + 3dx2 + -1dy + -3dy2 = 0 Solving -5dx + -4dxy + 3dx2 + -1dy + -3dy2 = 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(-5x + -4xy + 3x2 + -1y + -3y2) = 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 '(-5x + -4xy + 3x2 + -1y + -3y2)' equal to zero and attempt to solve: Simplifying -5x + -4xy + 3x2 + -1y + -3y2 = 0 Solving -5x + -4xy + 3x2 + -1y + -3y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '5x' to each side of the equation. -5x + -4xy + 3x2 + -1y + 5x + -3y2 = 0 + 5x Reorder the terms: -5x + 5x + -4xy + 3x2 + -1y + -3y2 = 0 + 5x Combine like terms: -5x + 5x = 0 0 + -4xy + 3x2 + -1y + -3y2 = 0 + 5x -4xy + 3x2 + -1y + -3y2 = 0 + 5x Remove the zero: -4xy + 3x2 + -1y + -3y2 = 5x Add '4xy' to each side of the equation. -4xy + 3x2 + -1y + 4xy + -3y2 = 5x + 4xy Reorder the terms: -4xy + 4xy + 3x2 + -1y + -3y2 = 5x + 4xy Combine like terms: -4xy + 4xy = 0 0 + 3x2 + -1y + -3y2 = 5x + 4xy 3x2 + -1y + -3y2 = 5x + 4xy Add '-3x2' to each side of the equation. 3x2 + -1y + -3x2 + -3y2 = 5x + 4xy + -3x2 Reorder the terms: 3x2 + -3x2 + -1y + -3y2 = 5x + 4xy + -3x2 Combine like terms: 3x2 + -3x2 = 0 0 + -1y + -3y2 = 5x + 4xy + -3x2 -1y + -3y2 = 5x + 4xy + -3x2 Add 'y' to each side of the equation. -1y + y + -3y2 = 5x + 4xy + -3x2 + y Combine like terms: -1y + y = 0 0 + -3y2 = 5x + 4xy + -3x2 + y -3y2 = 5x + 4xy + -3x2 + y Add '3y2' to each side of the equation. -3y2 + 3y2 = 5x + 4xy + -3x2 + y + 3y2 Combine like terms: -3y2 + 3y2 = 0 0 = 5x + 4xy + -3x2 + y + 3y2 Simplifying 0 = 5x + 4xy + -3x2 + y + 3y2 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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