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Simplifying (2y2 + -6xy) * dx(3xy + -4x2) * dy = 0 Reorder the terms: (-6xy + 2y2) * dx(3xy + -4x2) * dy = 0 Reorder the terms for easier multiplication: dx * dy(-6xy + 2y2)(3xy + -4x2) = 0 Multiply dx * dy d2xy(-6xy + 2y2)(3xy + -4x2) = 0 Multiply (-6xy + 2y2) * (3xy + -4x2) d2xy(-6xy * (3xy + -4x2) + 2y2 * (3xy + -4x2)) = 0 d2xy((3xy * -6xy + -4x2 * -6xy) + 2y2 * (3xy + -4x2)) = 0 d2xy((-18x2y2 + 24x3y) + 2y2 * (3xy + -4x2)) = 0 d2xy(-18x2y2 + 24x3y + (3xy * 2y2 + -4x2 * 2y2)) = 0 d2xy(-18x2y2 + 24x3y + (6xy3 + -8x2y2)) = 0 Reorder the terms: d2xy(6xy3 + -18x2y2 + -8x2y2 + 24x3y) = 0 Combine like terms: -18x2y2 + -8x2y2 = -26x2y2 d2xy(6xy3 + -26x2y2 + 24x3y) = 0 (6xy3 * d2xy + -26x2y2 * d2xy + 24x3y * d2xy) = 0 (6d2x2y4 + -26d2x3y3 + 24d2x4y2) = 0 Solving 6d2x2y4 + -26d2x3y3 + 24d2x4y2 = 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), '2d2x2y2'. 2d2x2y2(3y2 + -13xy + 12x2) = 0 Factor a trinomial. 2d2x2y2((y + -3x)(3y + -4x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'd2x2y2' equal to zero and attempt to solve: Simplifying d2x2y2 = 0 Solving d2x2y2 = 0 Move all terms containing d to the left, all other terms to the right. Simplifying d2x2y2 = 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 '(y + -3x)' equal to zero and attempt to solve: Simplifying y + -3x = 0 Reorder the terms: -3x + y = 0 Solving -3x + y = 0 Move all terms containing d to the left, all other terms to the right. Add '3x' to each side of the equation. -3x + 3x + y = 0 + 3x Combine like terms: -3x + 3x = 0 0 + y = 0 + 3x y = 0 + 3x Remove the zero: y = 3x Add '-1y' to each side of the equation. y + -1y = 3x + -1y Combine like terms: y + -1y = 0 0 = 3x + -1y Simplifying 0 = 3x + -1y The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(3y + -4x)' equal to zero and attempt to solve: Simplifying 3y + -4x = 0 Reorder the terms: -4x + 3y = 0 Solving -4x + 3y = 0 Move all terms containing d to the left, all other terms to the right. Add '4x' to each side of the equation. -4x + 4x + 3y = 0 + 4x Combine like terms: -4x + 4x = 0 0 + 3y = 0 + 4x 3y = 0 + 4x Remove the zero: 3y = 4x Add '-3y' to each side of the equation. 3y + -3y = 4x + -3y Combine like terms: 3y + -3y = 0 0 = 4x + -3y Simplifying 0 = 4x + -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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