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Simplifying (9y + 5) * x(4y + 5) = 125xy Reorder the terms: (5 + 9y) * x(4y + 5) = 125xy Reorder the terms: (5 + 9y) * x(5 + 4y) = 125xy Reorder the terms for easier multiplication: x(5 + 9y)(5 + 4y) = 125xy Multiply (5 + 9y) * (5 + 4y) x(5(5 + 4y) + 9y * (5 + 4y)) = 125xy x((5 * 5 + 4y * 5) + 9y * (5 + 4y)) = 125xy x((25 + 20y) + 9y * (5 + 4y)) = 125xy x(25 + 20y + (5 * 9y + 4y * 9y)) = 125xy x(25 + 20y + (45y + 36y2)) = 125xy Combine like terms: 20y + 45y = 65y x(25 + 65y + 36y2) = 125xy (25 * x + 65y * x + 36y2 * x) = 125xy (25x + 65xy + 36xy2) = 125xy Solving 25x + 65xy + 36xy2 = 125xy Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-125xy' to each side of the equation. 25x + 65xy + -125xy + 36xy2 = 125xy + -125xy Combine like terms: 65xy + -125xy = -60xy 25x + -60xy + 36xy2 = 125xy + -125xy Combine like terms: 125xy + -125xy = 0 25x + -60xy + 36xy2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(25 + -60y + 36y2) = 0 Factor a trinomial. x((5 + -6y)(5 + -6y)) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(5 + -6y)' equal to zero and attempt to solve: Simplifying 5 + -6y = 0 Solving 5 + -6y = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -6y = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -6y = 0 + -5 -6y = 0 + -5 Combine like terms: 0 + -5 = -5 -6y = -5 Add '6y' to each side of the equation. -6y + 6y = -5 + 6y Combine like terms: -6y + 6y = 0 0 = -5 + 6y Simplifying 0 = -5 + 6y 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 '(5 + -6y)' equal to zero and attempt to solve: Simplifying 5 + -6y = 0 Solving 5 + -6y = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -6y = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -6y = 0 + -5 -6y = 0 + -5 Combine like terms: 0 + -5 = -5 -6y = -5 Add '6y' to each side of the equation. -6y + 6y = -5 + 6y Combine like terms: -6y + 6y = 0 0 = -5 + 6y Simplifying 0 = -5 + 6y The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
x = {0}
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