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Simplifying (2x2 + 3y2 + -7) * dx + -1(3x2 + 2y2 + -8) * dy = 0 Reorder the terms: (-7 + 2x2 + 3y2) * dx + -1(3x2 + 2y2 + -8) * dy = 0 Reorder the terms for easier multiplication: dx(-7 + 2x2 + 3y2) + -1(3x2 + 2y2 + -8) * dy = 0 (-7 * dx + 2x2 * dx + 3y2 * dx) + -1(3x2 + 2y2 + -8) * dy = 0 Reorder the terms: (-7dx + 3dxy2 + 2dx3) + -1(3x2 + 2y2 + -8) * dy = 0 (-7dx + 3dxy2 + 2dx3) + -1(3x2 + 2y2 + -8) * dy = 0 Reorder the terms: -7dx + 3dxy2 + 2dx3 + -1(-8 + 3x2 + 2y2) * dy = 0 Reorder the terms for easier multiplication: -7dx + 3dxy2 + 2dx3 + -1dy(-8 + 3x2 + 2y2) = 0 -7dx + 3dxy2 + 2dx3 + (-8 * -1dy + 3x2 * -1dy + 2y2 * -1dy) = 0 Reorder the terms: -7dx + 3dxy2 + 2dx3 + (-3dx2y + 8dy + -2dy3) = 0 -7dx + 3dxy2 + 2dx3 + (-3dx2y + 8dy + -2dy3) = 0 Reorder the terms: -7dx + 3dxy2 + -3dx2y + 2dx3 + 8dy + -2dy3 = 0 Solving -7dx + 3dxy2 + -3dx2y + 2dx3 + 8dy + -2dy3 = 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), 'd'. d(-7x + 3xy2 + -3x2y + 2x3 + 8y + -2y3) = 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 '(-7x + 3xy2 + -3x2y + 2x3 + 8y + -2y3)' equal to zero and attempt to solve: Simplifying -7x + 3xy2 + -3x2y + 2x3 + 8y + -2y3 = 0 Solving -7x + 3xy2 + -3x2y + 2x3 + 8y + -2y3 = 0 Move all terms containing d to the left, all other terms to the right. Add '7x' to each side of the equation. -7x + 3xy2 + -3x2y + 2x3 + 8y + 7x + -2y3 = 0 + 7x Reorder the terms: -7x + 7x + 3xy2 + -3x2y + 2x3 + 8y + -2y3 = 0 + 7x Combine like terms: -7x + 7x = 0 0 + 3xy2 + -3x2y + 2x3 + 8y + -2y3 = 0 + 7x 3xy2 + -3x2y + 2x3 + 8y + -2y3 = 0 + 7x Remove the zero: 3xy2 + -3x2y + 2x3 + 8y + -2y3 = 7x Add '-3xy2' to each side of the equation. 3xy2 + -3x2y + 2x3 + 8y + -3xy2 + -2y3 = 7x + -3xy2 Reorder the terms: 3xy2 + -3xy2 + -3x2y + 2x3 + 8y + -2y3 = 7x + -3xy2 Combine like terms: 3xy2 + -3xy2 = 0 0 + -3x2y + 2x3 + 8y + -2y3 = 7x + -3xy2 -3x2y + 2x3 + 8y + -2y3 = 7x + -3xy2 Add '3x2y' to each side of the equation. -3x2y + 2x3 + 8y + 3x2y + -2y3 = 7x + -3xy2 + 3x2y Reorder the terms: -3x2y + 3x2y + 2x3 + 8y + -2y3 = 7x + -3xy2 + 3x2y Combine like terms: -3x2y + 3x2y = 0 0 + 2x3 + 8y + -2y3 = 7x + -3xy2 + 3x2y 2x3 + 8y + -2y3 = 7x + -3xy2 + 3x2y Add '-2x3' to each side of the equation. 2x3 + 8y + -2x3 + -2y3 = 7x + -3xy2 + 3x2y + -2x3 Reorder the terms: 2x3 + -2x3 + 8y + -2y3 = 7x + -3xy2 + 3x2y + -2x3 Combine like terms: 2x3 + -2x3 = 0 0 + 8y + -2y3 = 7x + -3xy2 + 3x2y + -2x3 8y + -2y3 = 7x + -3xy2 + 3x2y + -2x3 Add '-8y' to each side of the equation. 8y + -8y + -2y3 = 7x + -3xy2 + 3x2y + -2x3 + -8y Combine like terms: 8y + -8y = 0 0 + -2y3 = 7x + -3xy2 + 3x2y + -2x3 + -8y -2y3 = 7x + -3xy2 + 3x2y + -2x3 + -8y Add '2y3' to each side of the equation. -2y3 + 2y3 = 7x + -3xy2 + 3x2y + -2x3 + -8y + 2y3 Combine like terms: -2y3 + 2y3 = 0 0 = 7x + -3xy2 + 3x2y + -2x3 + -8y + 2y3 Simplifying 0 = 7x + -3xy2 + 3x2y + -2x3 + -8y + 2y3 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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