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Simplifying 3x(2 + y2) * dx = 2y(4 + x2) * dy Reorder the terms for easier multiplication: 3x * dx(2 + y2) = 2y(4 + x2) * dy Multiply x * dx 3dx2(2 + y2) = 2y(4 + x2) * dy (2 * 3dx2 + y2 * 3dx2) = 2y(4 + x2) * dy (6dx2 + 3dx2y2) = 2y(4 + x2) * dy Reorder the terms for easier multiplication: 6dx2 + 3dx2y2 = 2y * dy(4 + x2) Multiply y * dy 6dx2 + 3dx2y2 = 2dy2(4 + x2) 6dx2 + 3dx2y2 = (4 * 2dy2 + x2 * 2dy2) Reorder the terms: 6dx2 + 3dx2y2 = (2dx2y2 + 8dy2) 6dx2 + 3dx2y2 = (2dx2y2 + 8dy2) Solving 6dx2 + 3dx2y2 = 2dx2y2 + 8dy2 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-2dx2y2' to each side of the equation. 6dx2 + 3dx2y2 + -2dx2y2 = 2dx2y2 + -2dx2y2 + 8dy2 Combine like terms: 3dx2y2 + -2dx2y2 = 1dx2y2 6dx2 + 1dx2y2 = 2dx2y2 + -2dx2y2 + 8dy2 Combine like terms: 2dx2y2 + -2dx2y2 = 0 6dx2 + 1dx2y2 = 0 + 8dy2 6dx2 + 1dx2y2 = 8dy2 Add '-8dy2' to each side of the equation. 6dx2 + 1dx2y2 + -8dy2 = 8dy2 + -8dy2 Combine like terms: 8dy2 + -8dy2 = 0 6dx2 + 1dx2y2 + -8dy2 = 0 Factor out the Greatest Common Factor (GCF), 'd'. d(6x2 + x2y2 + -8y2) = 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 '(6x2 + x2y2 + -8y2)' equal to zero and attempt to solve: Simplifying 6x2 + x2y2 + -8y2 = 0 Solving 6x2 + x2y2 + -8y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-6x2' to each side of the equation. 6x2 + x2y2 + -6x2 + -8y2 = 0 + -6x2 Reorder the terms: 6x2 + -6x2 + x2y2 + -8y2 = 0 + -6x2 Combine like terms: 6x2 + -6x2 = 0 0 + x2y2 + -8y2 = 0 + -6x2 x2y2 + -8y2 = 0 + -6x2 Remove the zero: x2y2 + -8y2 = -6x2 Add '-1x2y2' to each side of the equation. x2y2 + -1x2y2 + -8y2 = -6x2 + -1x2y2 Combine like terms: x2y2 + -1x2y2 = 0 0 + -8y2 = -6x2 + -1x2y2 -8y2 = -6x2 + -1x2y2 Add '8y2' to each side of the equation. -8y2 + 8y2 = -6x2 + -1x2y2 + 8y2 Combine like terms: -8y2 + 8y2 = 0 0 = -6x2 + -1x2y2 + 8y2 Simplifying 0 = -6x2 + -1x2y2 + 8y2 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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