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Simplifying (3x + 8xy2) * dx + (2x + 6x2y) * dy = 0 Reorder the terms for easier multiplication: dx(3x + 8xy2) + (2x + 6x2y) * dy = 0 (3x * dx + 8xy2 * dx) + (2x + 6x2y) * dy = 0 (3dx2 + 8dx2y2) + (2x + 6x2y) * dy = 0 Reorder the terms for easier multiplication: 3dx2 + 8dx2y2 + dy(2x + 6x2y) = 0 3dx2 + 8dx2y2 + (2x * dy + 6x2y * dy) = 0 3dx2 + 8dx2y2 + (2dxy + 6dx2y2) = 0 Reorder the terms: 2dxy + 3dx2 + 8dx2y2 + 6dx2y2 = 0 Combine like terms: 8dx2y2 + 6dx2y2 = 14dx2y2 2dxy + 3dx2 + 14dx2y2 = 0 Solving 2dxy + 3dx2 + 14dx2y2 = 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), 'dx'. dx(2y + 3x + 14xy2) = 0Subproblem 1
Set the factor 'dx' equal to zero and attempt to solve: Simplifying dx = 0 Solving dx = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dx = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(2y + 3x + 14xy2)' equal to zero and attempt to solve: Simplifying 2y + 3x + 14xy2 = 0 Reorder the terms: 3x + 14xy2 + 2y = 0 Solving 3x + 14xy2 + 2y = 0 Move all terms containing d to the left, all other terms to the right. Add '-3x' to each side of the equation. 3x + 14xy2 + -3x + 2y = 0 + -3x Reorder the terms: 3x + -3x + 14xy2 + 2y = 0 + -3x Combine like terms: 3x + -3x = 0 0 + 14xy2 + 2y = 0 + -3x 14xy2 + 2y = 0 + -3x Remove the zero: 14xy2 + 2y = -3x Add '-14xy2' to each side of the equation. 14xy2 + -14xy2 + 2y = -3x + -14xy2 Combine like terms: 14xy2 + -14xy2 = 0 0 + 2y = -3x + -14xy2 2y = -3x + -14xy2 Add '-2y' to each side of the equation. 2y + -2y = -3x + -14xy2 + -2y Combine like terms: 2y + -2y = 0 0 = -3x + -14xy2 + -2y Simplifying 0 = -3x + -14xy2 + -2y The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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