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Simplifying (2x3 + 3xy2 + -7x) * dx + (-3x2y + -2y3 + 8y) * dy = 0 Reorder the terms: (-7x + 3xy2 + 2x3) * dx + (-3x2y + -2y3 + 8y) * dy = 0 Reorder the terms for easier multiplication: dx(-7x + 3xy2 + 2x3) + (-3x2y + -2y3 + 8y) * dy = 0 (-7x * dx + 3xy2 * dx + 2x3 * dx) + (-3x2y + -2y3 + 8y) * dy = 0 (-7dx2 + 3dx2y2 + 2dx4) + (-3x2y + -2y3 + 8y) * dy = 0 Reorder the terms: -7dx2 + 3dx2y2 + 2dx4 + (-3x2y + 8y + -2y3) * dy = 0 Reorder the terms for easier multiplication: -7dx2 + 3dx2y2 + 2dx4 + dy(-3x2y + 8y + -2y3) = 0 -7dx2 + 3dx2y2 + 2dx4 + (-3x2y * dy + 8y * dy + -2y3 * dy) = 0 -7dx2 + 3dx2y2 + 2dx4 + (-3dx2y2 + 8dy2 + -2dy4) = 0 Reorder the terms: -7dx2 + 3dx2y2 + -3dx2y2 + 2dx4 + 8dy2 + -2dy4 = 0 Combine like terms: 3dx2y2 + -3dx2y2 = 0 -7dx2 + 0 + 2dx4 + 8dy2 + -2dy4 = 0 -7dx2 + 2dx4 + 8dy2 + -2dy4 = 0 Solving -7dx2 + 2dx4 + 8dy2 + -2dy4 = 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(-7x2 + 2x4 + 8y2 + -2y4) = 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 '(-7x2 + 2x4 + 8y2 + -2y4)' equal to zero and attempt to solve: Simplifying -7x2 + 2x4 + 8y2 + -2y4 = 0 Solving -7x2 + 2x4 + 8y2 + -2y4 = 0 Move all terms containing d to the left, all other terms to the right. Add '7x2' to each side of the equation. -7x2 + 2x4 + 8y2 + 7x2 + -2y4 = 0 + 7x2 Reorder the terms: -7x2 + 7x2 + 2x4 + 8y2 + -2y4 = 0 + 7x2 Combine like terms: -7x2 + 7x2 = 0 0 + 2x4 + 8y2 + -2y4 = 0 + 7x2 2x4 + 8y2 + -2y4 = 0 + 7x2 Remove the zero: 2x4 + 8y2 + -2y4 = 7x2 Add '-2x4' to each side of the equation. 2x4 + 8y2 + -2x4 + -2y4 = 7x2 + -2x4 Reorder the terms: 2x4 + -2x4 + 8y2 + -2y4 = 7x2 + -2x4 Combine like terms: 2x4 + -2x4 = 0 0 + 8y2 + -2y4 = 7x2 + -2x4 8y2 + -2y4 = 7x2 + -2x4 Add '-8y2' to each side of the equation. 8y2 + -8y2 + -2y4 = 7x2 + -2x4 + -8y2 Combine like terms: 8y2 + -8y2 = 0 0 + -2y4 = 7x2 + -2x4 + -8y2 -2y4 = 7x2 + -2x4 + -8y2 Add '2y4' to each side of the equation. -2y4 + 2y4 = 7x2 + -2x4 + -8y2 + 2y4 Combine like terms: -2y4 + 2y4 = 0 0 = 7x2 + -2x4 + -8y2 + 2y4 Simplifying 0 = 7x2 + -2x4 + -8y2 + 2y4 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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