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Simplifying (2x + 7y) * dx(2x + 5y) * dy = 0 Reorder the terms for easier multiplication: dx * dy(2x + 7y)(2x + 5y) = 0 Multiply dx * dy d2xy(2x + 7y)(2x + 5y) = 0 Multiply (2x + 7y) * (2x + 5y) d2xy(2x * (2x + 5y) + 7y * (2x + 5y)) = 0 d2xy((2x * 2x + 5y * 2x) + 7y * (2x + 5y)) = 0 Reorder the terms: d2xy((10xy + 4x2) + 7y * (2x + 5y)) = 0 d2xy((10xy + 4x2) + 7y * (2x + 5y)) = 0 d2xy(10xy + 4x2 + (2x * 7y + 5y * 7y)) = 0 d2xy(10xy + 4x2 + (14xy + 35y2)) = 0 Reorder the terms: d2xy(10xy + 14xy + 4x2 + 35y2) = 0 Combine like terms: 10xy + 14xy = 24xy d2xy(24xy + 4x2 + 35y2) = 0 (24xy * d2xy + 4x2 * d2xy + 35y2 * d2xy) = 0 Reorder the terms: (35d2xy3 + 24d2x2y2 + 4d2x3y) = 0 (35d2xy3 + 24d2x2y2 + 4d2x3y) = 0 Solving 35d2xy3 + 24d2x2y2 + 4d2x3y = 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), 'd2xy'. d2xy(35y2 + 24xy + 4x2) = 0 Factor a trinomial. d2xy((7y + 2x)(5y + 2x)) = 0Subproblem 1
Set the factor 'd2xy' equal to zero and attempt to solve: Simplifying d2xy = 0 Solving d2xy = 0 Move all terms containing d to the left, all other terms to the right. Simplifying d2xy = 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 '(7y + 2x)' equal to zero and attempt to solve: Simplifying 7y + 2x = 0 Reorder the terms: 2x + 7y = 0 Solving 2x + 7y = 0 Move all terms containing d to the left, all other terms to the right. Add '-2x' to each side of the equation. 2x + -2x + 7y = 0 + -2x Combine like terms: 2x + -2x = 0 0 + 7y = 0 + -2x 7y = 0 + -2x Remove the zero: 7y = -2x Add '-7y' to each side of the equation. 7y + -7y = -2x + -7y Combine like terms: 7y + -7y = 0 0 = -2x + -7y Simplifying 0 = -2x + -7y The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(5y + 2x)' equal to zero and attempt to solve: Simplifying 5y + 2x = 0 Reorder the terms: 2x + 5y = 0 Solving 2x + 5y = 0 Move all terms containing d to the left, all other terms to the right. Add '-2x' to each side of the equation. 2x + -2x + 5y = 0 + -2x Combine like terms: 2x + -2x = 0 0 + 5y = 0 + -2x 5y = 0 + -2x Remove the zero: 5y = -2x Add '-5y' to each side of the equation. 5y + -5y = -2x + -5y Combine like terms: 5y + -5y = 0 0 = -2x + -5y Simplifying 0 = -2x + -5y 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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