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Simplifying (2x + -2y2) * dx + (12x2 + -4xy) * dy = 0 Reorder the terms for easier multiplication: dx(2x + -2y2) + (12x2 + -4xy) * dy = 0 (2x * dx + -2y2 * dx) + (12x2 + -4xy) * dy = 0 Reorder the terms: (-2dxy2 + 2dx2) + (12x2 + -4xy) * dy = 0 (-2dxy2 + 2dx2) + (12x2 + -4xy) * dy = 0 Reorder the terms: -2dxy2 + 2dx2 + (-4xy + 12x2) * dy = 0 Reorder the terms for easier multiplication: -2dxy2 + 2dx2 + dy(-4xy + 12x2) = 0 -2dxy2 + 2dx2 + (-4xy * dy + 12x2 * dy) = 0 -2dxy2 + 2dx2 + (-4dxy2 + 12dx2y) = 0 Reorder the terms: -2dxy2 + -4dxy2 + 2dx2 + 12dx2y = 0 Combine like terms: -2dxy2 + -4dxy2 = -6dxy2 -6dxy2 + 2dx2 + 12dx2y = 0 Solving -6dxy2 + 2dx2 + 12dx2y = 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), '2dx'. 2dx(-3y2 + x + 6xy) = 0 Ignore the factor 2.Subproblem 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 '(-3y2 + x + 6xy)' equal to zero and attempt to solve: Simplifying -3y2 + x + 6xy = 0 Reorder the terms: x + 6xy + -3y2 = 0 Solving x + 6xy + -3y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-1x' to each side of the equation. x + 6xy + -1x + -3y2 = 0 + -1x Reorder the terms: x + -1x + 6xy + -3y2 = 0 + -1x Combine like terms: x + -1x = 0 0 + 6xy + -3y2 = 0 + -1x 6xy + -3y2 = 0 + -1x Remove the zero: 6xy + -3y2 = -1x Add '-6xy' to each side of the equation. 6xy + -6xy + -3y2 = -1x + -6xy Combine like terms: 6xy + -6xy = 0 0 + -3y2 = -1x + -6xy -3y2 = -1x + -6xy Add '3y2' to each side of the equation. -3y2 + 3y2 = -1x + -6xy + 3y2 Combine like terms: -3y2 + 3y2 = 0 0 = -1x + -6xy + 3y2 Simplifying 0 = -1x + -6xy + 3y2 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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