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Simplifying (6xy2 + 6x2y) * dx + (12x2y + 6x3) * dy = 0 Reorder the terms for easier multiplication: dx(6xy2 + 6x2y) + (12x2y + 6x3) * dy = 0 (6xy2 * dx + 6x2y * dx) + (12x2y + 6x3) * dy = 0 (6dx2y2 + 6dx3y) + (12x2y + 6x3) * dy = 0 Reorder the terms for easier multiplication: 6dx2y2 + 6dx3y + dy(12x2y + 6x3) = 0 6dx2y2 + 6dx3y + (12x2y * dy + 6x3 * dy) = 0 6dx2y2 + 6dx3y + (12dx2y2 + 6dx3y) = 0 Reorder the terms: 6dx2y2 + 12dx2y2 + 6dx3y + 6dx3y = 0 Combine like terms: 6dx2y2 + 12dx2y2 = 18dx2y2 18dx2y2 + 6dx3y + 6dx3y = 0 Combine like terms: 6dx3y + 6dx3y = 12dx3y 18dx2y2 + 12dx3y = 0 Solving 18dx2y2 + 12dx3y = 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), '6dx2y'. 6dx2y(3y + 2x) = 0 Ignore the factor 6.Subproblem 1
Set the factor 'dx2y' equal to zero and attempt to solve: Simplifying dx2y = 0 Solving dx2y = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dx2y = 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 '(3y + 2x)' equal to zero and attempt to solve: Simplifying 3y + 2x = 0 Reorder the terms: 2x + 3y = 0 Solving 2x + 3y = 0 Move all terms containing d to the left, all other terms to the right. Add '-2x' to each side of the equation. 2x + -2x + 3y = 0 + -2x Combine like terms: 2x + -2x = 0 0 + 3y = 0 + -2x 3y = 0 + -2x Remove the zero: 3y = -2x Add '-3y' to each side of the equation. 3y + -3y = -2x + -3y Combine like terms: 3y + -3y = 0 0 = -2x + -3y Simplifying 0 = -2x + -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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