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Simplifying 12xy * dx + (4y + 18x2) * dy = 0 Multiply xy * dx 12dx2y + (4y + 18x2) * dy = 0 Reorder the terms: 12dx2y + (18x2 + 4y) * dy = 0 Reorder the terms for easier multiplication: 12dx2y + dy(18x2 + 4y) = 0 12dx2y + (18x2 * dy + 4y * dy) = 0 12dx2y + (18dx2y + 4dy2) = 0 Combine like terms: 12dx2y + 18dx2y = 30dx2y 30dx2y + 4dy2 = 0 Solving 30dx2y + 4dy2 = 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), '2dy'. 2dy(15x2 + 2y) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'dy' equal to zero and attempt to solve: Simplifying dy = 0 Solving dy = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dy = 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 '(15x2 + 2y)' equal to zero and attempt to solve: Simplifying 15x2 + 2y = 0 Solving 15x2 + 2y = 0 Move all terms containing d to the left, all other terms to the right. Add '-15x2' to each side of the equation. 15x2 + -15x2 + 2y = 0 + -15x2 Combine like terms: 15x2 + -15x2 = 0 0 + 2y = 0 + -15x2 2y = 0 + -15x2 Remove the zero: 2y = -15x2 Add '-2y' to each side of the equation. 2y + -2y = -15x2 + -2y Combine like terms: 2y + -2y = 0 0 = -15x2 + -2y Simplifying 0 = -15x2 + -2y 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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