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