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Simplifying (3x + g + -15) * dx + (6x + 2y + -5) * dy = 0 Reorder the terms: (-15 + g + 3x) * dx + (6x + 2y + -5) * dy = 0 Reorder the terms for easier multiplication: dx(-15 + g + 3x) + (6x + 2y + -5) * dy = 0 (-15 * dx + g * dx + 3x * dx) + (6x + 2y + -5) * dy = 0 Reorder the terms: (dgx + -15dx + 3dx2) + (6x + 2y + -5) * dy = 0 (dgx + -15dx + 3dx2) + (6x + 2y + -5) * dy = 0 Reorder the terms: dgx + -15dx + 3dx2 + (-5 + 6x + 2y) * dy = 0 Reorder the terms for easier multiplication: dgx + -15dx + 3dx2 + dy(-5 + 6x + 2y) = 0 dgx + -15dx + 3dx2 + (-5 * dy + 6x * dy + 2y * dy) = 0 Reorder the terms: dgx + -15dx + 3dx2 + (6dxy + -5dy + 2dy2) = 0 dgx + -15dx + 3dx2 + (6dxy + -5dy + 2dy2) = 0 Reorder the terms: dgx + -15dx + 6dxy + 3dx2 + -5dy + 2dy2 = 0 Solving dgx + -15dx + 6dxy + 3dx2 + -5dy + 2dy2 = 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(gx + -15x + 6xy + 3x2 + -5y + 2y2) = 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 '(gx + -15x + 6xy + 3x2 + -5y + 2y2)' equal to zero and attempt to solve: Simplifying gx + -15x + 6xy + 3x2 + -5y + 2y2 = 0 Solving gx + -15x + 6xy + 3x2 + -5y + 2y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-1gx' to each side of the equation. gx + -15x + 6xy + 3x2 + -5y + -1gx + 2y2 = 0 + -1gx Reorder the terms: gx + -1gx + -15x + 6xy + 3x2 + -5y + 2y2 = 0 + -1gx Combine like terms: gx + -1gx = 0 0 + -15x + 6xy + 3x2 + -5y + 2y2 = 0 + -1gx -15x + 6xy + 3x2 + -5y + 2y2 = 0 + -1gx Remove the zero: -15x + 6xy + 3x2 + -5y + 2y2 = -1gx Add '15x' to each side of the equation. -15x + 6xy + 3x2 + -5y + 15x + 2y2 = -1gx + 15x Reorder the terms: -15x + 15x + 6xy + 3x2 + -5y + 2y2 = -1gx + 15x Combine like terms: -15x + 15x = 0 0 + 6xy + 3x2 + -5y + 2y2 = -1gx + 15x 6xy + 3x2 + -5y + 2y2 = -1gx + 15x Add '-6xy' to each side of the equation. 6xy + 3x2 + -5y + -6xy + 2y2 = -1gx + 15x + -6xy Reorder the terms: 6xy + -6xy + 3x2 + -5y + 2y2 = -1gx + 15x + -6xy Combine like terms: 6xy + -6xy = 0 0 + 3x2 + -5y + 2y2 = -1gx + 15x + -6xy 3x2 + -5y + 2y2 = -1gx + 15x + -6xy Add '-3x2' to each side of the equation. 3x2 + -5y + -3x2 + 2y2 = -1gx + 15x + -6xy + -3x2 Reorder the terms: 3x2 + -3x2 + -5y + 2y2 = -1gx + 15x + -6xy + -3x2 Combine like terms: 3x2 + -3x2 = 0 0 + -5y + 2y2 = -1gx + 15x + -6xy + -3x2 -5y + 2y2 = -1gx + 15x + -6xy + -3x2 Add '5y' to each side of the equation. -5y + 5y + 2y2 = -1gx + 15x + -6xy + -3x2 + 5y Combine like terms: -5y + 5y = 0 0 + 2y2 = -1gx + 15x + -6xy + -3x2 + 5y 2y2 = -1gx + 15x + -6xy + -3x2 + 5y Add '-2y2' to each side of the equation. 2y2 + -2y2 = -1gx + 15x + -6xy + -3x2 + 5y + -2y2 Combine like terms: 2y2 + -2y2 = 0 0 = -1gx + 15x + -6xy + -3x2 + 5y + -2y2 Simplifying 0 = -1gx + 15x + -6xy + -3x2 + 5y + -2y2 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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