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Simplifying (4y + 2x + -5) * dx + (6y + 4x + -1) * dy = 0y(-1) * 2 Reorder the terms: (-5 + 2x + 4y) * dx + (6y + 4x + -1) * dy = 0y(-1) * 2 Reorder the terms for easier multiplication: dx(-5 + 2x + 4y) + (6y + 4x + -1) * dy = 0y(-1) * 2 (-5 * dx + 2x * dx + 4y * dx) + (6y + 4x + -1) * dy = 0y(-1) * 2 Reorder the terms: (-5dx + 4dxy + 2dx2) + (6y + 4x + -1) * dy = 0y(-1) * 2 (-5dx + 4dxy + 2dx2) + (6y + 4x + -1) * dy = 0y(-1) * 2 Reorder the terms: -5dx + 4dxy + 2dx2 + (-1 + 4x + 6y) * dy = 0y(-1) * 2 Reorder the terms for easier multiplication: -5dx + 4dxy + 2dx2 + dy(-1 + 4x + 6y) = 0y(-1) * 2 -5dx + 4dxy + 2dx2 + (-1 * dy + 4x * dy + 6y * dy) = 0y(-1) * 2 Reorder the terms: -5dx + 4dxy + 2dx2 + (4dxy + -1dy + 6dy2) = 0y(-1) * 2 -5dx + 4dxy + 2dx2 + (4dxy + -1dy + 6dy2) = 0y(-1) * 2 Reorder the terms: -5dx + 4dxy + 4dxy + 2dx2 + -1dy + 6dy2 = 0y(-1) * 2 Combine like terms: 4dxy + 4dxy = 8dxy -5dx + 8dxy + 2dx2 + -1dy + 6dy2 = 0y(-1) * 2 Reorder the terms for easier multiplication: -5dx + 8dxy + 2dx2 + -1dy + 6dy2 = 0 * -1 * 2y Multiply 0 * -1 -5dx + 8dxy + 2dx2 + -1dy + 6dy2 = 0 * 2y Anything times zero is zero. -5dx + 8dxy + 2dx2 + -1dy + 6dy2 = 0 * 2y Solving -5dx + 8dxy + 2dx2 + -1dy + 6dy2 = 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 + 8xy + 2x2 + -1y + 6y2) = 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 + 8xy + 2x2 + -1y + 6y2)' equal to zero and attempt to solve: Simplifying -5x + 8xy + 2x2 + -1y + 6y2 = 0 Solving -5x + 8xy + 2x2 + -1y + 6y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '5x' to each side of the equation. -5x + 8xy + 2x2 + -1y + 5x + 6y2 = 0 + 5x Reorder the terms: -5x + 5x + 8xy + 2x2 + -1y + 6y2 = 0 + 5x Combine like terms: -5x + 5x = 0 0 + 8xy + 2x2 + -1y + 6y2 = 0 + 5x 8xy + 2x2 + -1y + 6y2 = 0 + 5x Remove the zero: 8xy + 2x2 + -1y + 6y2 = 5x Add '-8xy' to each side of the equation. 8xy + 2x2 + -1y + -8xy + 6y2 = 5x + -8xy Reorder the terms: 8xy + -8xy + 2x2 + -1y + 6y2 = 5x + -8xy Combine like terms: 8xy + -8xy = 0 0 + 2x2 + -1y + 6y2 = 5x + -8xy 2x2 + -1y + 6y2 = 5x + -8xy Add '-2x2' to each side of the equation. 2x2 + -1y + -2x2 + 6y2 = 5x + -8xy + -2x2 Reorder the terms: 2x2 + -2x2 + -1y + 6y2 = 5x + -8xy + -2x2 Combine like terms: 2x2 + -2x2 = 0 0 + -1y + 6y2 = 5x + -8xy + -2x2 -1y + 6y2 = 5x + -8xy + -2x2 Add 'y' to each side of the equation. -1y + y + 6y2 = 5x + -8xy + -2x2 + y Combine like terms: -1y + y = 0 0 + 6y2 = 5x + -8xy + -2x2 + y 6y2 = 5x + -8xy + -2x2 + y Add '-6y2' to each side of the equation. 6y2 + -6y2 = 5x + -8xy + -2x2 + y + -6y2 Combine like terms: 6y2 + -6y2 = 0 0 = 5x + -8xy + -2x2 + y + -6y2 Simplifying 0 = 5x + -8xy + -2x2 + y + -6y2 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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