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Simplifying (dx + -1dy)(6dx + -1dy) = 0 Multiply (dx + -1dy) * (6dx + -1dy) (dx(6dx + -1dy) + -1dy * (6dx + -1dy)) = 0 ((6dx * dx + -1dy * dx) + -1dy * (6dx + -1dy)) = 0 Reorder the terms: ((-1d2xy + 6d2x2) + -1dy * (6dx + -1dy)) = 0 ((-1d2xy + 6d2x2) + -1dy * (6dx + -1dy)) = 0 (-1d2xy + 6d2x2 + (6dx * -1dy + -1dy * -1dy)) = 0 (-1d2xy + 6d2x2 + (-6d2xy + 1d2y2)) = 0 Reorder the terms: (-1d2xy + -6d2xy + 6d2x2 + 1d2y2) = 0 Combine like terms: -1d2xy + -6d2xy = -7d2xy (-7d2xy + 6d2x2 + 1d2y2) = 0 Solving -7d2xy + 6d2x2 + 1d2y2 = 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), 'd2'. d2(-7xy + 6x2 + y2) = 0 Factor a trinomial. d2((x + -1y)(6x + -1y)) = 0Subproblem 1
Set the factor 'd2' equal to zero and attempt to solve: Simplifying d2 = 0 Solving d2 = 0 Move all terms containing d to the left, all other terms to the right. Simplifying d2 = 0 Take the square root of each side: d = {0}Subproblem 2
Set the factor '(x + -1y)' equal to zero and attempt to solve: Simplifying x + -1y = 0 Solving x + -1y = 0 Move all terms containing d to the left, all other terms to the right. Add '-1x' to each side of the equation. x + -1x + -1y = 0 + -1x Combine like terms: x + -1x = 0 0 + -1y = 0 + -1x -1y = 0 + -1x Remove the zero: -1y = -1x Add 'y' to each side of the equation. -1y + y = -1x + y Combine like terms: -1y + y = 0 0 = -1x + y Simplifying 0 = -1x + y 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 '(6x + -1y)' equal to zero and attempt to solve: Simplifying 6x + -1y = 0 Solving 6x + -1y = 0 Move all terms containing d to the left, all other terms to the right. Add '-6x' to each side of the equation. 6x + -6x + -1y = 0 + -6x Combine like terms: 6x + -6x = 0 0 + -1y = 0 + -6x -1y = 0 + -6x Remove the zero: -1y = -6x Add 'y' to each side of the equation. -1y + y = -6x + y Combine like terms: -1y + y = 0 0 = -6x + y Simplifying 0 = -6x + y 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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