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Simplifying (4y + -2x + -3) * dy + (4x + 2y + 3) * dy = 0 Reorder the terms: (-3 + -2x + 4y) * dy + (4x + 2y + 3) * dy = 0 Reorder the terms for easier multiplication: dy(-3 + -2x + 4y) + (4x + 2y + 3) * dy = 0 (-3 * dy + -2x * dy + 4y * dy) + (4x + 2y + 3) * dy = 0 Reorder the terms: (-2dxy + -3dy + 4dy2) + (4x + 2y + 3) * dy = 0 (-2dxy + -3dy + 4dy2) + (4x + 2y + 3) * dy = 0 Reorder the terms: -2dxy + -3dy + 4dy2 + (3 + 4x + 2y) * dy = 0 Reorder the terms for easier multiplication: -2dxy + -3dy + 4dy2 + dy(3 + 4x + 2y) = 0 -2dxy + -3dy + 4dy2 + (3 * dy + 4x * dy + 2y * dy) = 0 Reorder the terms: -2dxy + -3dy + 4dy2 + (4dxy + 3dy + 2dy2) = 0 -2dxy + -3dy + 4dy2 + (4dxy + 3dy + 2dy2) = 0 Reorder the terms: -2dxy + 4dxy + -3dy + 3dy + 4dy2 + 2dy2 = 0 Combine like terms: -2dxy + 4dxy = 2dxy 2dxy + -3dy + 3dy + 4dy2 + 2dy2 = 0 Combine like terms: -3dy + 3dy = 0 2dxy + 0 + 4dy2 + 2dy2 = 0 2dxy + 4dy2 + 2dy2 = 0 Combine like terms: 4dy2 + 2dy2 = 6dy2 2dxy + 6dy2 = 0 Solving 2dxy + 6dy2 = 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), '2dy'. 2dy(x + 3y) = 0 Ignore the factor 2.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 + 3y)' equal to zero and attempt to solve: Simplifying x + 3y = 0 Solving x + 3y = 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 + 3y = 0 + -1x Combine like terms: x + -1x = 0 0 + 3y = 0 + -1x 3y = 0 + -1x Remove the zero: 3y = -1x Add '-3y' to each side of the equation. 3y + -3y = -1x + -3y Combine like terms: 3y + -3y = 0 0 = -1x + -3y Simplifying 0 = -1x + -3y 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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