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Simplifying (4x + 3y + -15) * dx + (2x + y + -7) * dy = 0 Reorder the terms: (-15 + 4x + 3y) * dx + (2x + y + -7) * dy = 0 Reorder the terms for easier multiplication: dx(-15 + 4x + 3y) + (2x + y + -7) * dy = 0 (-15 * dx + 4x * dx + 3y * dx) + (2x + y + -7) * dy = 0 Reorder the terms: (-15dx + 3dxy + 4dx2) + (2x + y + -7) * dy = 0 (-15dx + 3dxy + 4dx2) + (2x + y + -7) * dy = 0 Reorder the terms: -15dx + 3dxy + 4dx2 + (-7 + 2x + y) * dy = 0 Reorder the terms for easier multiplication: -15dx + 3dxy + 4dx2 + dy(-7 + 2x + y) = 0 -15dx + 3dxy + 4dx2 + (-7 * dy + 2x * dy + y * dy) = 0 Reorder the terms: -15dx + 3dxy + 4dx2 + (2dxy + -7dy + dy2) = 0 -15dx + 3dxy + 4dx2 + (2dxy + -7dy + dy2) = 0 Reorder the terms: -15dx + 3dxy + 2dxy + 4dx2 + -7dy + dy2 = 0 Combine like terms: 3dxy + 2dxy = 5dxy -15dx + 5dxy + 4dx2 + -7dy + dy2 = 0 Solving -15dx + 5dxy + 4dx2 + -7dy + dy2 = 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(-15x + 5xy + 4x2 + -7y + y2) = 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 '(-15x + 5xy + 4x2 + -7y + y2)' equal to zero and attempt to solve: Simplifying -15x + 5xy + 4x2 + -7y + y2 = 0 Solving -15x + 5xy + 4x2 + -7y + y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '15x' to each side of the equation. -15x + 5xy + 4x2 + -7y + 15x + y2 = 0 + 15x Reorder the terms: -15x + 15x + 5xy + 4x2 + -7y + y2 = 0 + 15x Combine like terms: -15x + 15x = 0 0 + 5xy + 4x2 + -7y + y2 = 0 + 15x 5xy + 4x2 + -7y + y2 = 0 + 15x Remove the zero: 5xy + 4x2 + -7y + y2 = 15x Add '-5xy' to each side of the equation. 5xy + 4x2 + -7y + -5xy + y2 = 15x + -5xy Reorder the terms: 5xy + -5xy + 4x2 + -7y + y2 = 15x + -5xy Combine like terms: 5xy + -5xy = 0 0 + 4x2 + -7y + y2 = 15x + -5xy 4x2 + -7y + y2 = 15x + -5xy Add '-4x2' to each side of the equation. 4x2 + -7y + -4x2 + y2 = 15x + -5xy + -4x2 Reorder the terms: 4x2 + -4x2 + -7y + y2 = 15x + -5xy + -4x2 Combine like terms: 4x2 + -4x2 = 0 0 + -7y + y2 = 15x + -5xy + -4x2 -7y + y2 = 15x + -5xy + -4x2 Add '7y' to each side of the equation. -7y + 7y + y2 = 15x + -5xy + -4x2 + 7y Combine like terms: -7y + 7y = 0 0 + y2 = 15x + -5xy + -4x2 + 7y y2 = 15x + -5xy + -4x2 + 7y Add '-1y2' to each side of the equation. y2 + -1y2 = 15x + -5xy + -4x2 + 7y + -1y2 Combine like terms: y2 + -1y2 = 0 0 = 15x + -5xy + -4x2 + 7y + -1y2 Simplifying 0 = 15x + -5xy + -4x2 + 7y + -1y2 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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