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Simplifying (6x + 8y2) * dx(16xy + -5) * dy = 0 Reorder the terms: (6x + 8y2) * dx(-5 + 16xy) * dy = 0 Reorder the terms for easier multiplication: dx * dy(6x + 8y2)(-5 + 16xy) = 0 Multiply dx * dy d2xy(6x + 8y2)(-5 + 16xy) = 0 Multiply (6x + 8y2) * (-5 + 16xy) d2xy(6x * (-5 + 16xy) + 8y2 * (-5 + 16xy)) = 0 d2xy((-5 * 6x + 16xy * 6x) + 8y2 * (-5 + 16xy)) = 0 d2xy((-30x + 96x2y) + 8y2 * (-5 + 16xy)) = 0 d2xy(-30x + 96x2y + (-5 * 8y2 + 16xy * 8y2)) = 0 Reorder the terms: d2xy(-30x + 96x2y + (128xy3 + -40y2)) = 0 d2xy(-30x + 96x2y + (128xy3 + -40y2)) = 0 Reorder the terms: d2xy(-30x + 128xy3 + 96x2y + -40y2) = 0 d2xy(-30x + 128xy3 + 96x2y + -40y2) = 0 (-30x * d2xy + 128xy3 * d2xy + 96x2y * d2xy + -40y2 * d2xy) = 0 Reorder the terms: (-40d2xy3 + -30d2x2y + 128d2x2y4 + 96d2x3y2) = 0 (-40d2xy3 + -30d2x2y + 128d2x2y4 + 96d2x3y2) = 0 Solving -40d2xy3 + -30d2x2y + 128d2x2y4 + 96d2x3y2 = 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), '2d2xy'. 2d2xy(-20y2 + -15x + 64xy3 + 48x2y) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'd2xy' equal to zero and attempt to solve: Simplifying d2xy = 0 Solving d2xy = 0 Move all terms containing d to the left, all other terms to the right. Simplifying d2xy = 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 '(-20y2 + -15x + 64xy3 + 48x2y)' equal to zero and attempt to solve: Simplifying -20y2 + -15x + 64xy3 + 48x2y = 0 Reorder the terms: -15x + 64xy3 + 48x2y + -20y2 = 0 Solving -15x + 64xy3 + 48x2y + -20y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '15x' to each side of the equation. -15x + 64xy3 + 48x2y + 15x + -20y2 = 0 + 15x Reorder the terms: -15x + 15x + 64xy3 + 48x2y + -20y2 = 0 + 15x Combine like terms: -15x + 15x = 0 0 + 64xy3 + 48x2y + -20y2 = 0 + 15x 64xy3 + 48x2y + -20y2 = 0 + 15x Remove the zero: 64xy3 + 48x2y + -20y2 = 15x Add '-64xy3' to each side of the equation. 64xy3 + 48x2y + -64xy3 + -20y2 = 15x + -64xy3 Reorder the terms: 64xy3 + -64xy3 + 48x2y + -20y2 = 15x + -64xy3 Combine like terms: 64xy3 + -64xy3 = 0 0 + 48x2y + -20y2 = 15x + -64xy3 48x2y + -20y2 = 15x + -64xy3 Add '-48x2y' to each side of the equation. 48x2y + -48x2y + -20y2 = 15x + -64xy3 + -48x2y Combine like terms: 48x2y + -48x2y = 0 0 + -20y2 = 15x + -64xy3 + -48x2y -20y2 = 15x + -64xy3 + -48x2y Add '20y2' to each side of the equation. -20y2 + 20y2 = 15x + -64xy3 + -48x2y + 20y2 Combine like terms: -20y2 + 20y2 = 0 0 = 15x + -64xy3 + -48x2y + 20y2 Simplifying 0 = 15x + -64xy3 + -48x2y + 20y2 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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