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Simplifying (2y + -1) * dy = (3x + 1) * dx Reorder the terms: (-1 + 2y) * dy = (3x + 1) * dx Reorder the terms for easier multiplication: dy(-1 + 2y) = (3x + 1) * dx (-1 * dy + 2y * dy) = (3x + 1) * dx (-1dy + 2dy2) = (3x + 1) * dx Reorder the terms: -1dy + 2dy2 = (1 + 3x) * dx Reorder the terms for easier multiplication: -1dy + 2dy2 = dx(1 + 3x) -1dy + 2dy2 = (1 * dx + 3x * dx) -1dy + 2dy2 = (1dx + 3dx2) Solving -1dy + 2dy2 = 1dx + 3dx2 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-1dx' to each side of the equation. -1dy + -1dx + 2dy2 = 1dx + -1dx + 3dx2 Reorder the terms: -1dx + -1dy + 2dy2 = 1dx + -1dx + 3dx2 Combine like terms: 1dx + -1dx = 0 -1dx + -1dy + 2dy2 = 0 + 3dx2 -1dx + -1dy + 2dy2 = 3dx2 Add '-3dx2' to each side of the equation. -1dx + -1dy + -3dx2 + 2dy2 = 3dx2 + -3dx2 Reorder the terms: -1dx + -3dx2 + -1dy + 2dy2 = 3dx2 + -3dx2 Combine like terms: 3dx2 + -3dx2 = 0 -1dx + -3dx2 + -1dy + 2dy2 = 0 Factor out the Greatest Common Factor (GCF), 'd'. d(-1x + -3x2 + -1y + 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 '(-1x + -3x2 + -1y + 2y2)' equal to zero and attempt to solve: Simplifying -1x + -3x2 + -1y + 2y2 = 0 Solving -1x + -3x2 + -1y + 2y2 = 0 Move all terms containing d to the left, all other terms to the right. Add 'x' to each side of the equation. -1x + -3x2 + -1y + x + 2y2 = 0 + x Reorder the terms: -1x + x + -3x2 + -1y + 2y2 = 0 + x Combine like terms: -1x + x = 0 0 + -3x2 + -1y + 2y2 = 0 + x -3x2 + -1y + 2y2 = 0 + x Remove the zero: -3x2 + -1y + 2y2 = x Add '3x2' to each side of the equation. -3x2 + -1y + 3x2 + 2y2 = x + 3x2 Reorder the terms: -3x2 + 3x2 + -1y + 2y2 = x + 3x2 Combine like terms: -3x2 + 3x2 = 0 0 + -1y + 2y2 = x + 3x2 -1y + 2y2 = x + 3x2 Add 'y' to each side of the equation. -1y + y + 2y2 = x + 3x2 + y Combine like terms: -1y + y = 0 0 + 2y2 = x + 3x2 + y 2y2 = x + 3x2 + y Add '-2y2' to each side of the equation. 2y2 + -2y2 = x + 3x2 + y + -2y2 Combine like terms: 2y2 + -2y2 = 0 0 = x + 3x2 + y + -2y2 Simplifying 0 = x + 3x2 + y + -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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