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Simplifying (2x + 3y + 1) * dx = -1(4x + 6y + -5) * dy Reorder the terms: (1 + 2x + 3y) * dx = -1(4x + 6y + -5) * dy Reorder the terms for easier multiplication: dx(1 + 2x + 3y) = -1(4x + 6y + -5) * dy (1 * dx + 2x * dx + 3y * dx) = -1(4x + 6y + -5) * dy Reorder the terms: (1dx + 3dxy + 2dx2) = -1(4x + 6y + -5) * dy (1dx + 3dxy + 2dx2) = -1(4x + 6y + -5) * dy Reorder the terms: 1dx + 3dxy + 2dx2 = -1(-5 + 4x + 6y) * dy Reorder the terms for easier multiplication: 1dx + 3dxy + 2dx2 = -1dy(-5 + 4x + 6y) 1dx + 3dxy + 2dx2 = (-5 * -1dy + 4x * -1dy + 6y * -1dy) Reorder the terms: 1dx + 3dxy + 2dx2 = (-4dxy + 5dy + -6dy2) 1dx + 3dxy + 2dx2 = (-4dxy + 5dy + -6dy2) Solving 1dx + 3dxy + 2dx2 = -4dxy + 5dy + -6dy2 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '4dxy' to each side of the equation. 1dx + 3dxy + 4dxy + 2dx2 = -4dxy + 5dy + 4dxy + -6dy2 Combine like terms: 3dxy + 4dxy = 7dxy 1dx + 7dxy + 2dx2 = -4dxy + 5dy + 4dxy + -6dy2 Reorder the terms: 1dx + 7dxy + 2dx2 = -4dxy + 4dxy + 5dy + -6dy2 Combine like terms: -4dxy + 4dxy = 0 1dx + 7dxy + 2dx2 = 0 + 5dy + -6dy2 1dx + 7dxy + 2dx2 = 5dy + -6dy2 Add '-5dy' to each side of the equation. 1dx + 7dxy + 2dx2 + -5dy = 5dy + -5dy + -6dy2 Combine like terms: 5dy + -5dy = 0 1dx + 7dxy + 2dx2 + -5dy = 0 + -6dy2 1dx + 7dxy + 2dx2 + -5dy = -6dy2 Add '6dy2' to each side of the equation. 1dx + 7dxy + 2dx2 + -5dy + 6dy2 = -6dy2 + 6dy2 Combine like terms: -6dy2 + 6dy2 = 0 1dx + 7dxy + 2dx2 + -5dy + 6dy2 = 0 Factor out the Greatest Common Factor (GCF), 'd'. d(x + 7xy + 2x2 + -5y + 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 '(x + 7xy + 2x2 + -5y + 6y2)' equal to zero and attempt to solve: Simplifying x + 7xy + 2x2 + -5y + 6y2 = 0 Solving x + 7xy + 2x2 + -5y + 6y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-1x' to each side of the equation. x + 7xy + 2x2 + -5y + -1x + 6y2 = 0 + -1x Reorder the terms: x + -1x + 7xy + 2x2 + -5y + 6y2 = 0 + -1x Combine like terms: x + -1x = 0 0 + 7xy + 2x2 + -5y + 6y2 = 0 + -1x 7xy + 2x2 + -5y + 6y2 = 0 + -1x Remove the zero: 7xy + 2x2 + -5y + 6y2 = -1x Add '-7xy' to each side of the equation. 7xy + 2x2 + -5y + -7xy + 6y2 = -1x + -7xy Reorder the terms: 7xy + -7xy + 2x2 + -5y + 6y2 = -1x + -7xy Combine like terms: 7xy + -7xy = 0 0 + 2x2 + -5y + 6y2 = -1x + -7xy 2x2 + -5y + 6y2 = -1x + -7xy Add '-2x2' to each side of the equation. 2x2 + -5y + -2x2 + 6y2 = -1x + -7xy + -2x2 Reorder the terms: 2x2 + -2x2 + -5y + 6y2 = -1x + -7xy + -2x2 Combine like terms: 2x2 + -2x2 = 0 0 + -5y + 6y2 = -1x + -7xy + -2x2 -5y + 6y2 = -1x + -7xy + -2x2 Add '5y' to each side of the equation. -5y + 5y + 6y2 = -1x + -7xy + -2x2 + 5y Combine like terms: -5y + 5y = 0 0 + 6y2 = -1x + -7xy + -2x2 + 5y 6y2 = -1x + -7xy + -2x2 + 5y Add '-6y2' to each side of the equation. 6y2 + -6y2 = -1x + -7xy + -2x2 + 5y + -6y2 Combine like terms: 6y2 + -6y2 = 0 0 = -1x + -7xy + -2x2 + 5y + -6y2 Simplifying 0 = -1x + -7xy + -2x2 + 5y + -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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