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